Edit Profile (opens in new tab) Borgs, Christian Compute Distance To: Compute Author ID: borgs.christian Published as: Borgs, Christian; Borgs, C. Homepage: https://www.microsoft.com/en-us/research/people/borgs/?from=http%3A%2F%2Fresearc... External Links: MGP · Wikidata · Google Scholar · dblp Documents Indexed: 82 Publications since 1986 1 Contribution as Editor Co-Authors: 79 Co-Authors with 80 Joint Publications 2,413 Co-Co-Authors all top 5 Co-Authors 3 single-authored 68 Chayes, Jennifer Tour 9 Kotecký, Roman 7 Lovász, László 7 Teng, Shang-Hua 6 Berger, Noam 6 Cohn, Henry Lee 5 Bollobás, Béla 5 Mirrokni, Vahab S. 5 Sós, Vera Turán 5 Spencer, Joel H. 5 Vesztergombi, Katalin L. 4 Mertens, Stephan 4 Pittel, Boris G. 4 Riordan, Oliver Maxim 4 Slade, Gordon 4 van der Hofstad, Remco W. 3 Andersen, Reid 3 Bayati, Mohsen Fathollah 3 Biskup, Marek 3 Brautbar, Michael 3 Imbrie, John Z. 3 King, Christopher K. 3 Saberi, Amin 3 Tetali, Prasad 2 Fröhlich, Jürg Martin 2 Hopcroft, John Edward H. 2 Immorlica, Nicole 2 Kalai, Adam Tauman 2 Kesten, Harry 2 Kleinberg, Robert D. 2 Madras, Neal 2 Montanari, Andrea 2 Nair, Chandra 2 Papadimitriou, Christos Harilaos 2 Waxler, Roger 2 Zecchina, Riccardo 2 Zhao, Yufei 1 Balcan, Maria-Florina 1 Baldassi, Carlo 1 Braverman, Mark 1 Chaudhari, Pratik 1 Choromanska, Anna 1 Dhara, Souvik 1 Doroudi, Sherwin 1 Dyer, Martin E. 1 Gamarnik, David 1 Ganesh, Ayalvadi J. 1 Ganguly, Shirshendu 1 Harchol-Balter, Mor 1 Helmuth, Tyler 1 Holden, Nina 1 Hopcraft, John 1 Jȩdrzejewski, Janusz 1 Kahn, Jeff D. 1 Kanoria, Yash 1 Kanoria, Yashodhan 1 Karrer, Brian 1 Kim, Jeong Han 1 Kleinwaks, L. J. 1 LeCun, Yann 1 Lovász, László Miklós 1 Lucier, Brendan 1 Marple, Adrian 1 Medved’, Igor 1 Meeder, Brendan 1 Nill, Florian 1 Perkins, Will 1 Randall, Dana J. 1 Ravi, Ramamoorthi 1 Reagans, Ray 1 Sagun, Levent 1 Sayedi, Amin 1 Sen, Subhabrata 1 Soatto, Stefano 1 Szegedy, Balázs 1 Ueltschi, Daniel 1 Veitch, Victor 1 Wilson, David Bruce 1 Xu, Kuang all top 5 Serials 11 Communications in Mathematical Physics 10 Random Structures & Algorithms 8 Journal of Statistical Physics 6 The Annals of Probability 3 Journal of Mathematical Physics 2 Journal of Physics A: Mathematical and General 2 Combinatorics, Probability and Computing 2 Internet Mathematics 1 Advances in Mathematics 1 The Annals of Statistics 1 Journal of Economic Theory 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Combinatorica 1 Probability Theory and Related Fields 1 SIAM Journal on Discrete Mathematics 1 Geometric and Functional Analysis. GAFA 1 Games and Economic Behavior 1 Nuclear Physics. B. Proceedings Supplements 1 Annals of Combinatorics 1 Annals of Mathematics. Second Series 1 Probability in the Engineering and Informational Sciences 1 Journal of Machine Learning Research (JMLR) 1 Journal of Statistical Mechanics: Theory and Experiment all top 5 Fields 35 Probability theory and stochastic processes (60-XX) 34 Combinatorics (05-XX) 34 Statistical mechanics, structure of matter (82-XX) 25 Computer science (68-XX) 10 Operations research, mathematical programming (90-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Statistics (62-XX) 4 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 77 Publications have been cited 1,224 times in 817 Documents Cited by ▼ Year ▼ Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing. Zbl 1213.05161Borgs, C.; Chayes, J. T.; Lovász, L.; Sós, V. T.; Vesztergombi, K. 182 2008 Convergent sequences of dense graphs. II. Multiway cuts and statistical physics. Zbl 1247.05124Borgs, Christian; Chayes, Jennifer T.; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 88 2012 Counting graph homomorphisms. Zbl 1129.05050Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 61 2006 Directed scale-free graphs. Zbl 1094.68605Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 54 2003 Moments of two-variable functions and the uniqueness of graph limits. Zbl 1223.05193Borgs, Christian; Chayes, Jennifer; Lovász, László 54 2010 On the spread of viruses on the Internet. Zbl 1297.68029Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 49 2005 The scaling window of the 2-SAT transition. Zbl 0979.68053Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B. 38 2001 Graph limits and parameter testing. Zbl 1301.68199Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin 37 2006 Random subgraphs of finite graphs. I: The scaling window under the triangle condition. Zbl 1076.05071Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 33 2005 Maximizing social influence in nearly optimal time. Zbl 1420.68248Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Lucier, Brendan 33 2014 Random subgraphs of finite graphs. II: The lace expansion and the triangle condition. Zbl 1079.05087Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 31 2005 The birth of the infinite cluster: Finite-size scaling in percolation. Zbl 1038.82035Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 31 2001 A unified approach to phase diagrams in field theory and statistical mechanics. Zbl 0668.60092Borgs, Christian; Imbrie, John Z. 29 1989 An \(L^p\) theory of sparse graph convergence. I: Limits, sparse random graph models, and power law distributions. Zbl 1417.05186Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 29 2019 An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence. Zbl 1386.05099Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 29 2018 Asymptotic behavior and distributional limits of preferential attachment graphs. Zbl 1296.60010Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 26 2014 Left and right convergence of graphs with bounded degree. Zbl 1257.05172Borgs, Christian; Chayes, Jennifer; Kahn, Jeff; Lovász, László 25 2013 Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube. Zbl 1121.05108Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 20 2006 Sparse exchangeable graphs and their limits via graphon processes. Zbl 1469.60158Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Holden, Nina 20 2018 Low temperature phase diagrams for quantum perturbations of classical spin systems. Zbl 0858.60097Borgs, C.; Kotecký, R.; Ueltschi, D. 18 1996 Limits of randomly grown graph sequences. Zbl 1229.05247Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera; Vesztergombi, Katalin 17 2011 Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point. Zbl 1250.60034Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad 16 2012 First to market is not everything: an analysis of preferential attachment with fitness. Zbl 1232.68018Borgs, Christian; Chayes, Jennifer 14 2007 Uniform boundedness of critical crossing probabilities implies hyperscaling. Zbl 0940.60089Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 14 1999 Gibbs states of graphical representations of the Potts model with external fields. Zbl 0977.82012Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 14 2000 Partition function zeros at first-order phase transitions: a general analysis. Zbl 1088.82010Biskup, M.; Borgs, C.; Chayes, J. T.; Kleinwaks, L. J.; Kotecký, R. 13 2004 Absence of zeros for the chromatic polynomial on bounded degree graphs. Zbl 1082.05034Borgs, Christian 13 2006 Partition function zeros at first-order phase transitions: Pirogov-Sinai theory. Zbl 1142.82328Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 12 2004 Entropy-SGD: biasing gradient descent into wide valleys. Zbl 1459.65091Chaudhari, Pratik; Choromanska, Anna; Soatto, Stefano; LeCun, Yann; Baldassi, Carlo; Borgs, Christian; Chayes, Jennifer; Sagun, Levent; Zecchina, Riccardo 12 2019 How to distribute antidote to control epidemics. Zbl 1247.05247Borgs, Christian; Chayes, Jennifer; Ganesh, Ayalvadi; Saberi, Amin 11 2010 Bargaining dynamics in exchange networks. Zbl 1314.91112Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Kanoria, Yash; Montanari, Andrea 11 2015 Special issue: Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl 0969.00035 11 2000 Percolation on dense graph sequences. Zbl 1190.60090Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 10 2010 The covariance matrix of the Potts model: a random cluster analysis. Zbl 1042.82510Borgs, C.; Chayes, J. T. 9 1996 Belief propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions. Zbl 1225.68130Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo 8 2011 The van den Berg-Kesten-Reimer inequality: a review. Zbl 1115.82320Borgs, C.; Chayes, J. T.; Randall, D. 8 1999 Degree distribution of the FKP network model. Zbl 1039.68510Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 8 2003 The myth of the folk theorem. Zbl 1207.91012Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 7 2010 Phase transition and finite-size scaling for the integer partitioning problem. Zbl 1014.05009Borgs, Christian; Chayes, Jennifer; Pittel, Boris 7 2001 Sampling perspectives on sparse exchangeable graphs. Zbl 1448.60025Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Veitch, Victor 7 2019 Phase diagram for the constrained integer partitioning problem. Zbl 1049.90073Borgs, C.; Chayes, J. T.; Mertens, S.; Pittel, B. 6 2004 First order phase transitions in unbounded spin systems. I: Construction of the phase diagram. Zbl 0689.60088Borgs, Christian; Waxler, Roger 5 1989 First order phase transitions in unbounded spin systems. II: Completeness of the phase diagram. Zbl 0719.60121Borgs, Christian; Waxler, Roger 5 1990 Proof of the local REM conjecture for number partitioning. II. Growing energy scales. Zbl 1160.05304Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 5 2009 Finite-size scaling and surface tension from effective one dimensional systems. Zbl 0754.60129Borgs, Christian; Imbrie, John Z. 5 1992 On the sampling problem for \(H\)-colorings on the hypercube lattice. Zbl 1074.05032Borgs, Christian; Chayes, Jennifer T.; Dyer, Martin; Tetali, Prasad 5 2004 Mean-field lattice trees. Zbl 0934.60089Borgs, Christian; Chayes, Jennifer; van der Hofstad, Remco; Slade, Gordon 5 1999 Convergent sequences of sparse graphs: a large deviations approach. Zbl 1370.05119Borgs, Christian; Chayes, Jennifer; Gamarnik, David 5 2017 Fast convergence of natural bargaining dynamics in exchange networks. Zbl 1377.91106Kanoria, Yashodhan; Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Montanari, Andrea 5 2011 Local computation of pagerank contributions. Zbl 1206.68346Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcroft, John; Mirrokni, Vahab; Teng, Shang-Hua 5 2008 The myth of the folk theorem. Zbl 1231.91006Borgs, Christian; Chayes, Jennifer; Immortica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 4 2008 Proof of the local REM conjecture for number partitioning. I: Constant energy scales. Zbl 1160.05303Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 4 2009 Surface-induced finite-size effects for first-order phase transitions. Zbl 1081.82517Borgs, C.; Kotecký, R. 4 1995 The optimal admission threshold in observable queues with state dependent pricing. Zbl 1302.90042Borgs, Christian; Chayes, Jennifer T.; Doroudi, Sherwin; Harchol-Balter, Mor; Xu, Kuang 4 2014 A sublinear time algorithm for PageRank computations. Zbl 1342.05181Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 4 2012 Confinement, deconfinement and freezing in lattice Yang-Mills theories with continuous time. Zbl 1223.81145Borgs, Christian 3 1988 The staggered charge-order phase of the extended Hubbard model in the atomic limit. Zbl 0946.81523Borgs, Christian; Jędrzejewski, Janusz; Kitecký, Roman 3 1996 Competition-induced preferential attachment. Zbl 1098.68009Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 3 2004 Degree distribution of competition-induced preferential attachment graphs. Zbl 1087.05050Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 3 2005 Symmetry breaking in Landau gauge. A comment to a paper by T. Kennedy and C. King. Zbl 0593.46062Borgs, Christian; Nill, Florian 3 1986 Sharp threshold and scaling window for the integer partitioning problem. Zbl 1323.68311Borgs, Christian; Chayes, Jennifer; Pittel, Boris 3 2001 Finite-size effects for the Potts model with weak boundary conditions. Zbl 1027.82008Borgs, C.; Kotecký, R.; Medved’, I. 3 2002 An axiomatic approach to community detection. Zbl 1334.91061Borgs, Christian; Chayes, Jennifer; Marple, Adrian; Teng, Shang-Hua 2 2016 Local computation of PageRank contributions. Zbl 1136.68316Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcraft, John; Mirrokni, Vahab S.; Teng, Shang-Hua 2 2007 Low temperature phase diagrams of fermionic lattice systems. Zbl 0979.82004Borgs, C.; Kotecký, R. 2 2000 Dobrushin states in quantum lattice systems. Zbl 0888.60093Borgs, C.; Chayes, J. T.; Fröhlich, J. 2 1997 Crossover finite-size scaling at first-order transitions. Zbl 0893.60075Borgs, Christian; Imbrie, John Z. 2 1992 Degree distribution of the FKP network model. Zbl 1149.90030Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 2 2007 Efficient sampling and counting algorithms for the Potts model on \(\mathbb{Z}^d\) at all temperatures. Zbl 07298284Borgs, Christian; Chayes, Jennifer; Helmuth, Tyler; Perkins, Will; Tetali, Prasad 2 2020 Finding endogenously formed communities. Zbl 1422.68203Balcan, Maria-Florina; Borgs, Christian; Braverman, Mark; Chayes, Jennifer; Teng, Shang-Hua 2 2013 Game-theoretic models of information overload in social networks. Zbl 1310.91034Borgs, Christian; Chayes, Jennifer; Karrer, Brian; Meeder, Brendan; Ravi, R.; Reagans, Ray; Sayedi, Amin 1 2010 Meissner phase for a model of oriented flux lines. Zbl 0877.60067Borgs, C.; Chayes, J. T.; King, C. 1 1995 Dobrushin states for classical spin systems with complex interactions. Zbl 0945.82516Borgs, C.; Chayes, J. T.; Fröhlich, J. 1 1997 Finite-size scaling of the mass-gap for first-order phase transitions. Zbl 0989.82509Borgs, Christian 1 1993 Anisotropic self-avoiding walks. Zbl 1052.82013Borgs, Christian; Chayes, Jennifer; King, Christopher; Madras, Neal 1 2000 Identifiability for graphexes and the weak kernel metric. Zbl 1443.05169Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Lovász, László Miklós 1 2019 Multiscale matrix sampling and sublinear-time PageRank computation. Zbl 1462.68008Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 1 2014 Efficient sampling and counting algorithms for the Potts model on \(\mathbb{Z}^d\) at all temperatures. Zbl 07298284Borgs, Christian; Chayes, Jennifer; Helmuth, Tyler; Perkins, Will; Tetali, Prasad 2 2020 An \(L^p\) theory of sparse graph convergence. I: Limits, sparse random graph models, and power law distributions. Zbl 1417.05186Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 29 2019 Entropy-SGD: biasing gradient descent into wide valleys. Zbl 1459.65091Chaudhari, Pratik; Choromanska, Anna; Soatto, Stefano; LeCun, Yann; Baldassi, Carlo; Borgs, Christian; Chayes, Jennifer; Sagun, Levent; Zecchina, Riccardo 12 2019 Sampling perspectives on sparse exchangeable graphs. Zbl 1448.60025Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Veitch, Victor 7 2019 Identifiability for graphexes and the weak kernel metric. Zbl 1443.05169Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Lovász, László Miklós 1 2019 An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence. Zbl 1386.05099Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 29 2018 Sparse exchangeable graphs and their limits via graphon processes. Zbl 1469.60158Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Holden, Nina 20 2018 Convergent sequences of sparse graphs: a large deviations approach. Zbl 1370.05119Borgs, Christian; Chayes, Jennifer; Gamarnik, David 5 2017 An axiomatic approach to community detection. Zbl 1334.91061Borgs, Christian; Chayes, Jennifer; Marple, Adrian; Teng, Shang-Hua 2 2016 Bargaining dynamics in exchange networks. Zbl 1314.91112Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Kanoria, Yash; Montanari, Andrea 11 2015 Maximizing social influence in nearly optimal time. Zbl 1420.68248Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Lucier, Brendan 33 2014 Asymptotic behavior and distributional limits of preferential attachment graphs. Zbl 1296.60010Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 26 2014 The optimal admission threshold in observable queues with state dependent pricing. Zbl 1302.90042Borgs, Christian; Chayes, Jennifer T.; Doroudi, Sherwin; Harchol-Balter, Mor; Xu, Kuang 4 2014 Multiscale matrix sampling and sublinear-time PageRank computation. Zbl 1462.68008Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 1 2014 Left and right convergence of graphs with bounded degree. Zbl 1257.05172Borgs, Christian; Chayes, Jennifer; Kahn, Jeff; Lovász, László 25 2013 Finding endogenously formed communities. Zbl 1422.68203Balcan, Maria-Florina; Borgs, Christian; Braverman, Mark; Chayes, Jennifer; Teng, Shang-Hua 2 2013 Convergent sequences of dense graphs. II. Multiway cuts and statistical physics. Zbl 1247.05124Borgs, Christian; Chayes, Jennifer T.; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 88 2012 Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point. Zbl 1250.60034Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad 16 2012 A sublinear time algorithm for PageRank computations. Zbl 1342.05181Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 4 2012 Limits of randomly grown graph sequences. Zbl 1229.05247Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera; Vesztergombi, Katalin 17 2011 Belief propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions. Zbl 1225.68130Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo 8 2011 Fast convergence of natural bargaining dynamics in exchange networks. Zbl 1377.91106Kanoria, Yashodhan; Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Montanari, Andrea 5 2011 Moments of two-variable functions and the uniqueness of graph limits. Zbl 1223.05193Borgs, Christian; Chayes, Jennifer; Lovász, László 54 2010 How to distribute antidote to control epidemics. Zbl 1247.05247Borgs, Christian; Chayes, Jennifer; Ganesh, Ayalvadi; Saberi, Amin 11 2010 Percolation on dense graph sequences. Zbl 1190.60090Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 10 2010 The myth of the folk theorem. Zbl 1207.91012Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 7 2010 Game-theoretic models of information overload in social networks. Zbl 1310.91034Borgs, Christian; Chayes, Jennifer; Karrer, Brian; Meeder, Brendan; Ravi, R.; Reagans, Ray; Sayedi, Amin 1 2010 Proof of the local REM conjecture for number partitioning. II. Growing energy scales. Zbl 1160.05304Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 5 2009 Proof of the local REM conjecture for number partitioning. I: Constant energy scales. Zbl 1160.05303Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 4 2009 Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing. Zbl 1213.05161Borgs, C.; Chayes, J. T.; Lovász, L.; Sós, V. T.; Vesztergombi, K. 182 2008 Local computation of pagerank contributions. Zbl 1206.68346Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcroft, John; Mirrokni, Vahab; Teng, Shang-Hua 5 2008 The myth of the folk theorem. Zbl 1231.91006Borgs, Christian; Chayes, Jennifer; Immortica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 4 2008 First to market is not everything: an analysis of preferential attachment with fitness. Zbl 1232.68018Borgs, Christian; Chayes, Jennifer 14 2007 Local computation of PageRank contributions. Zbl 1136.68316Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcraft, John; Mirrokni, Vahab S.; Teng, Shang-Hua 2 2007 Degree distribution of the FKP network model. Zbl 1149.90030Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 2 2007 Counting graph homomorphisms. Zbl 1129.05050Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 61 2006 Graph limits and parameter testing. Zbl 1301.68199Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin 37 2006 Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube. Zbl 1121.05108Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 20 2006 Absence of zeros for the chromatic polynomial on bounded degree graphs. Zbl 1082.05034Borgs, Christian 13 2006 On the spread of viruses on the Internet. Zbl 1297.68029Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 49 2005 Random subgraphs of finite graphs. I: The scaling window under the triangle condition. Zbl 1076.05071Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 33 2005 Random subgraphs of finite graphs. II: The lace expansion and the triangle condition. Zbl 1079.05087Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 31 2005 Degree distribution of competition-induced preferential attachment graphs. Zbl 1087.05050Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 3 2005 Partition function zeros at first-order phase transitions: a general analysis. Zbl 1088.82010Biskup, M.; Borgs, C.; Chayes, J. T.; Kleinwaks, L. J.; Kotecký, R. 13 2004 Partition function zeros at first-order phase transitions: Pirogov-Sinai theory. Zbl 1142.82328Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 12 2004 Phase diagram for the constrained integer partitioning problem. Zbl 1049.90073Borgs, C.; Chayes, J. T.; Mertens, S.; Pittel, B. 6 2004 On the sampling problem for \(H\)-colorings on the hypercube lattice. Zbl 1074.05032Borgs, Christian; Chayes, Jennifer T.; Dyer, Martin; Tetali, Prasad 5 2004 Competition-induced preferential attachment. Zbl 1098.68009Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 3 2004 Directed scale-free graphs. Zbl 1094.68605Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 54 2003 Degree distribution of the FKP network model. Zbl 1039.68510Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 8 2003 Finite-size effects for the Potts model with weak boundary conditions. Zbl 1027.82008Borgs, C.; Kotecký, R.; Medved’, I. 3 2002 The scaling window of the 2-SAT transition. Zbl 0979.68053Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B. 38 2001 The birth of the infinite cluster: Finite-size scaling in percolation. Zbl 1038.82035Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 31 2001 Phase transition and finite-size scaling for the integer partitioning problem. Zbl 1014.05009Borgs, Christian; Chayes, Jennifer; Pittel, Boris 7 2001 Sharp threshold and scaling window for the integer partitioning problem. Zbl 1323.68311Borgs, Christian; Chayes, Jennifer; Pittel, Boris 3 2001 Gibbs states of graphical representations of the Potts model with external fields. Zbl 0977.82012Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 14 2000 Special issue: Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl 0969.00035 11 2000 Low temperature phase diagrams of fermionic lattice systems. Zbl 0979.82004Borgs, C.; Kotecký, R. 2 2000 Anisotropic self-avoiding walks. Zbl 1052.82013Borgs, Christian; Chayes, Jennifer; King, Christopher; Madras, Neal 1 2000 Uniform boundedness of critical crossing probabilities implies hyperscaling. Zbl 0940.60089Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 14 1999 The van den Berg-Kesten-Reimer inequality: a review. Zbl 1115.82320Borgs, C.; Chayes, J. T.; Randall, D. 8 1999 Mean-field lattice trees. Zbl 0934.60089Borgs, Christian; Chayes, Jennifer; van der Hofstad, Remco; Slade, Gordon 5 1999 Dobrushin states in quantum lattice systems. Zbl 0888.60093Borgs, C.; Chayes, J. T.; Fröhlich, J. 2 1997 Dobrushin states for classical spin systems with complex interactions. Zbl 0945.82516Borgs, C.; Chayes, J. T.; Fröhlich, J. 1 1997 Low temperature phase diagrams for quantum perturbations of classical spin systems. Zbl 0858.60097Borgs, C.; Kotecký, R.; Ueltschi, D. 18 1996 The covariance matrix of the Potts model: a random cluster analysis. Zbl 1042.82510Borgs, C.; Chayes, J. T. 9 1996 The staggered charge-order phase of the extended Hubbard model in the atomic limit. Zbl 0946.81523Borgs, Christian; Jędrzejewski, Janusz; Kitecký, Roman 3 1996 Surface-induced finite-size effects for first-order phase transitions. Zbl 1081.82517Borgs, C.; Kotecký, R. 4 1995 Meissner phase for a model of oriented flux lines. Zbl 0877.60067Borgs, C.; Chayes, J. T.; King, C. 1 1995 Finite-size scaling of the mass-gap for first-order phase transitions. Zbl 0989.82509Borgs, Christian 1 1993 Finite-size scaling and surface tension from effective one dimensional systems. Zbl 0754.60129Borgs, Christian; Imbrie, John Z. 5 1992 Crossover finite-size scaling at first-order transitions. Zbl 0893.60075Borgs, Christian; Imbrie, John Z. 2 1992 First order phase transitions in unbounded spin systems. II: Completeness of the phase diagram. Zbl 0719.60121Borgs, Christian; Waxler, Roger 5 1990 A unified approach to phase diagrams in field theory and statistical mechanics. Zbl 0668.60092Borgs, Christian; Imbrie, John Z. 29 1989 First order phase transitions in unbounded spin systems. I: Construction of the phase diagram. Zbl 0689.60088Borgs, Christian; Waxler, Roger 5 1989 Confinement, deconfinement and freezing in lattice Yang-Mills theories with continuous time. Zbl 1223.81145Borgs, Christian 3 1988 Symmetry breaking in Landau gauge. A comment to a paper by T. Kennedy and C. King. Zbl 0593.46062Borgs, Christian; Nill, Florian 3 1986 all cited Publications top 5 cited Publications all top 5 Cited by 1,216 Authors 35 Borgs, Christian 30 van der Hofstad, Remco W. 27 Chayes, Jennifer Tour 17 Janson, Svante 17 Lovász, László 15 Nešetřil, Jaroslav 13 Král’, Daniel 13 Zhao, Yufei 12 Nachmias, Asaf 12 Szegedy, Balázs 11 Bollobás, Béla 11 Hladký, Jan 10 Biskup, Marek 10 Regts, Guus 10 Resnick, Sidney Ira 9 Hoppen, Carlos 8 Chayes, Lincoln 8 Kohayakawa, Yoshiharu 8 Riordan, Oliver Maxim 7 Fox, Jacob 7 Heydenreich, Markus 7 Kotecký, Roman 7 Lubetzky, Eyal 7 Medvedev, Georgi S. 7 Peres, Yuval 7 Sly, Allan 7 Wang, Tiandong 6 Bhattacharya, Bhaswar B. 6 Bolla, Marianna 6 Chatterjee, Sourav 6 Cohn, Henry Lee 6 Das, Bikramjit 6 Dembo, Amir 6 Lovász, László Miklós 6 Nolin, Pierre 6 Ossona de Mendez, Patrice 6 Pikhurko, Oleg 6 Pittel, Boris G. 6 Röllin, Adrian 6 Wu, Weili 5 Backhausz, Ágnes M. 5 Camia, Federico 5 Chung, Fan 5 Csikvári, Péter 5 Diaconis, Persi Warren 5 Ding, Jian 5 Doležal, Martin 5 Durrett, Richard Timothy 5 Fernández, Roberto 5 Fröhlich, Jürg Martin 5 Garijo, Delia 5 Goodall, Andrew J. 5 Hooghiemstra, Gerard 5 Jordan, Jonathan H. 5 Kozma, Gady 5 Sampaio, Rudini Menezes 5 Shojaei-Fard, Ali 5 Sós, Vera Turán 5 Sudan, Madhu 5 Sun, Nike 5 Ueltschi, Daniel 5 Vigoda, Eric 5 Wade, Andrew R. 5 Yin, Mei 4 Blanca, Antonio 4 Bodineau, Thierry 4 Braides, Andrea 4 den Hollander, Frank 4 Duminil-Copin, Hugo 4 Garavaglia, Alessandro 4 Glebov, Roman 4 Hulshof, Tim 4 Kunszenti-Kovács, Dávid 4 Li, Deying 4 Manolescu, Ioan 4 Montanari, Andrea 4 Mörters, Peter 4 Mukherjee, Sumit 4 Patel, Viresh 4 Penrose, Mathew D. 4 Perkins, Will 4 Pradelski, Bary S. R. 4 Radin, Charles 4 Sinclair, Alistair 4 Sivakoff, David 4 Slade, Gordon 4 Valesin, Daniel 4 van den Berg, Rob 4 Vesztergombi, Katalin L. 3 Alexander, Kenneth S. 3 Bachmann, Sven 3 Ben-Sasson, Eli 3 Bhamidi, Shankar 3 Bovier, Anton 3 Can, Van Hao 3 Caputo, Pietro 3 Chen, Wenping 3 Cooper, Jacob W. 3 D’Angelo, Gianlorenzo 3 Du, Ding-Zhu ...and 1,116 more Authors all top 5 Cited in 195 Serials 61 Journal of Statistical Physics 41 Random Structures & Algorithms 38 Communications in Mathematical Physics 32 European Journal of Combinatorics 28 The Annals of Probability 25 Theoretical Computer Science 25 Probability Theory and Related Fields 23 The Annals of Applied Probability 22 Combinatorics, Probability and Computing 13 Journal of Mathematical Physics 12 Stochastic Processes and their Applications 11 Journal of Applied Probability 10 Advances in Applied Probability 10 Advances in Mathematics 10 Journal of Combinatorial Theory. Series B 9 Discrete Mathematics 9 Algorithmica 9 SIAM Journal on Discrete Mathematics 8 Discrete Applied Mathematics 8 The Annals of Statistics 8 Electronic Journal of Probability 7 Physica A 7 Transactions of the American Mathematical Society 7 Combinatorica 7 Internet Mathematics 6 Israel Journal of Mathematics 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 6 Electronic Communications in Probability 6 Bernoulli 6 Journal of Statistical Mechanics: Theory and Experiment 6 Electronic Journal of Statistics 5 Artificial Intelligence 5 Reviews in Mathematical Physics 5 Applied Mathematics and Computation 5 Information Sciences 5 Geometric and Functional Analysis. GAFA 5 Computational Complexity 5 The Electronic Journal of Combinatorics 5 Extremes 5 Computer Science Review 4 Journal of Computer and System Sciences 4 Operations Research 4 SIAM Journal on Control and Optimization 4 Statistical Science 4 Theory of Computing Systems 4 Journal of Combinatorial Optimization 4 Methodology and Computing in Applied Probability 4 Journal of Machine Learning Research (JMLR) 3 Nuclear Physics. B 3 Physics Reports 3 Inventiones Mathematicae 3 Journal of Combinatorial Theory. Series A 3 Journal of Functional Analysis 3 Journal of Graph Theory 3 Proceedings of the American Mathematical Society 3 SIAM Journal on Computing 3 Acta Mathematica Hungarica 3 Journal of Theoretical Probability 3 Journal of the American Mathematical Society 3 Games and Economic Behavior 3 Linear Algebra and its Applications 3 Proceedings of the National Academy of Sciences of the United States of America 3 Journal of Nonlinear Science 3 Chaos 3 Annals of Mathematics. Second Series 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Discrete Analysis 3 SIAM Journal on Mathematics of Data Science 2 Archive for Rational Mechanics and Analysis 2 Communications on Pure and Applied Mathematics 2 Information Processing Letters 2 Journal of Mathematical Analysis and Applications 2 Rocky Mountain Journal of Mathematics 2 Chaos, Solitons and Fractals 2 Applied Mathematics and Optimization 2 International Journal of Game Theory 2 Journal of Algebra 2 Journal of Differential Equations 2 Journal of Economic Theory 2 Advances in Applied Mathematics 2 Physica D 2 Information and Computation 2 Bulletin of the American Mathematical Society. New Series 2 Economic Theory 2 Complexity 2 INFORMS Journal on Computing 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Annales Henri Poincaré 2 Stochastic Models 2 Oberwolfach Reports 2 Optimization Letters 2 Games 2 Journal of Theoretical Biology 2 Stochastic Systems 1 International Journal of Modern Physics B 1 Journal of the Franklin Institute 1 Letters in Mathematical Physics 1 Metrika 1 Nonlinearity ...and 95 more Serials all top 5 Cited in 47 Fields 423 Combinatorics (05-XX) 292 Probability theory and stochastic processes (60-XX) 227 Statistical mechanics, structure of matter (82-XX) 144 Computer science (68-XX) 79 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 62 Operations research, mathematical programming (90-XX) 47 Statistics (62-XX) 35 Quantum theory (81-XX) 34 Biology and other natural sciences (92-XX) 15 Functional analysis (46-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Measure and integration (28-XX) 12 Numerical analysis (65-XX) 11 Partial differential equations (35-XX) 10 Ordinary differential equations (34-XX) 9 Number theory (11-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Systems theory; control (93-XX) 9 Information and communication theory, circuits (94-XX) 8 Mathematical logic and foundations (03-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 5 Functions of a complex variable (30-XX) 5 Convex and discrete geometry (52-XX) 5 Mechanics of deformable solids (74-XX) 4 General and overarching topics; collections (00-XX) 4 Integral equations (45-XX) 4 Operator theory (47-XX) 3 History and biography (01-XX) 3 Group theory and generalizations (20-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Algebraic geometry (14-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Abstract harmonic analysis (43-XX) 2 General topology (54-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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