Edit Profile (opens in new tab) Merkl, Franz Compute Distance To: Compute Author ID: merkl.franz Published as: Merkl, Franz; Merkl, F. Documents Indexed: 37 Publications since 1994 1 Contribution as Editor · 2 Further Contributions Reviewing Activity: 1 Review Co-Authors: 20 Co-Authors with 35 Joint Publications 352 Co-Co-Authors all top 5 Co-Authors 3 single-authored 22 Rolles, Silke W. W. 4 Deckert, Dirk-André 4 Disertori, Margherita 4 Löwe, Matthias 3 Heydenreich, Markus 3 Wüthrich, Mario Valentin 2 Conache, Diana 2 Tarrès, Pierre 1 Anděl, Jiří 1 Bauerschmidt, Roland 1 Bosman, Johan 1 Cipra, Tomáš 1 Couveignes, Jean-Marc 1 de Jong, Robin 1 Devess, G. 1 Dürr, Detlef 1 Edixhoven, Bas 1 Ehrenberg, Dieter 1 Eichelsbacher, Peter 1 Elsner, Guido 1 Götze, Friedrich 1 Käschel, Joachim 1 Kösters, Holger 1 Laue, M. 1 Lommatzsch, Klaus 1 Malafeev, Oleg Alekseivich 1 Matzinger, Heinrich III 1 Melzer, Detlef 1 Meravý, Pavol 1 Mohammadi, Leila 1 Öry, Aniko 1 Petrosyan, Leon Aganesovich 1 Remke, Werner 1 Schottenloher, Martin 1 Sojka, Jan 1 Steckler, H. 1 Turnovec, Frantisek 1 Wagner, Herbert 1 Zerner, Martin P. W. all top 5 Serials 6 Electronic Journal of Probability 5 Probability Theory and Related Fields 4 The Annals of Probability 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Communications on Pure and Applied Mathematics 1 The Annals of Statistics 1 Inventiones Mathematicae 1 Statistica Neerlandica 1 Journal of Theoretical Probability 1 Stochastic Processes and their Applications 1 Electronic Communications in Probability 1 Mathematical Physics, Analysis and Geometry 1 Annales Henri Poincaré 1 Seminarbericht, Humboldt-Universität zu Berlin, Sektion Mathematik 1 Annals of Mathematics Studies 1 Springer Proceedings in Mathematics & Statistics all top 5 Fields 31 Probability theory and stochastic processes (60-XX) 21 Statistical mechanics, structure of matter (82-XX) 6 Quantum theory (81-XX) 3 Number theory (11-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 2 Statistics (62-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 30 Publications have been cited 217 times in 130 Documents Cited by ▼ Year ▼ Computational aspects of modular forms and Galois representations. How one can compute in polynomial time the value of Ramanujan’s tau at a prime. Zbl 1216.11004 21 2011 A zero-one law for planar random walks in random environment. Zbl 1016.60093Zerner, Martin P. W.; Merkl, Franz 19 2001 Recurrence of edge-reinforced random walk on a two-dimensional graph. Zbl 1180.82085Merkl, Franz; Rolles, Silke W. W. 15 2009 Moderate deviations for longest increasing subsequences: The upper tail. Zbl 1033.60035Löwe, Matthias; Merkl, Franz 15 2001 Moderate deviations for longest increasing subsequences: The lower tail. Zbl 1011.60007Löwe, Matthias; Merkl, Franz; Rolles, Silke 13 2002 Linearly edge-reinforced random walks. Zbl 1125.82014Merkl, Franz; Rolles, Silke W. W. 12 2006 Time-evolution of the external field problem in quantum electrodynamics. Zbl 1314.81164Deckert, D.-A.; Dürr, D.; Merkl, F.; Schottenloher, M. 11 2010 Reconstructing a multicolor random scenery seen along a random walk path with bounded jumps. Zbl 1064.60201Löwe, Matthias; Matzinger, Heinrich; Merkl, Franz 10 2004 Edge-reinforced random walk on a ladder. Zbl 1102.82010Merkl, Franz; Rolles, Silke W. W. 9 2005 A random environment for linearly edge-reinforced random walks on infinite graphs. Zbl 1116.60060Merkl, Franz; Rolles, Silke W. W. 8 2007 Spontaneous breaking of continuous rotational symmetry in two dimensions. Zbl 1191.60115Merkl, Franz; Rolles, Silke W. W. 8 2009 A supersymmetric approach to martingales related to the vertex-reinforced jump process. Zbl 1364.60068Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 8 2017 Edge-reinforced random walk on one-dimensional periodic graphs. Zbl 1186.82039Merkl, Franz; Rolles, Silke W. W. 7 2009 Spontaneous breaking of rotational symmetry in the presence of defects. Zbl 1307.60142Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W. 7 2014 Asymptotic behavior of edge-reinforced random walks. Zbl 1206.82082Merkl, Franz; Rolles, Silke W. W. 6 2007 Bounding a random environment bounding a random environment for two-dimensional edge-reinforced random walk. Zbl 1187.82051Merkl, Franz; Rolles, Silke W. W. 6 2008 Infinite volume asymptotics of the ground state energy in a scaled Poissonian potential. Zbl 0996.82036Merkl, Franz; Wüthrich, Mario V. 5 2002 Dirac equation with external potential and initial data on Cauchy surfaces. Zbl 1303.81075Deckert, D.-A.; Merkl, F. 5 2014 Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model. Zbl 1411.60147Merkl, Franz; Rolles, Silke W. W.; Tarrès, Pierre 4 2019 Recurrent random walks and the absence of continuous symmetry breaking on graphs. Zbl 0828.60055Merkl, Franz; Wagner, Herbert 4 1994 External field QED on Cauchy surfaces for varying electromagnetic fields. Zbl 1350.81031Deckert, D.-A.; Merkl, F. 4 2016 Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes. Zbl 1307.82013Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 4 2014 Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential. Zbl 1037.82022Merkl, Franz; Wüthrich, Mario V. 3 2001 A comparison of a nonlinear sigma model with general pinning and pinning at one point. Zbl 1336.60097Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 3 2016 The ’magic formula’ for linearly edge-reinforced random walks. Zbl 1146.60308Merkl, Franz; Öry, Aniko; Rolles, Silke W. W. 3 2008 Annealed survival asymptotics for Brownian motion in a scaled Poissonian potential. Zbl 1062.82022Merkl, Franz; Wüthrich, Mario V. 2 2001 Dislocation lines in three-dimensional solids at low temperature. Zbl 1479.60189Bauerschmidt, Roland; Conache, Diana; Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W. 2 2019 Quenched asymptotics of the ground state energy of random Schrödinger operators with scaled Gibbsian potentials. Zbl 1106.82016Merkl, Franz 1 2003 Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. Zbl 1405.60070Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 1 2019 Correlation inequalities for edge-reinforced random walk. Zbl 1243.60018Merkl, Franz; Rolles, Silke W. W. 1 2011 Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model. Zbl 1411.60147Merkl, Franz; Rolles, Silke W. W.; Tarrès, Pierre 4 2019 Dislocation lines in three-dimensional solids at low temperature. Zbl 1479.60189Bauerschmidt, Roland; Conache, Diana; Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W. 2 2019 Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model. Zbl 1405.60070Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 1 2019 A supersymmetric approach to martingales related to the vertex-reinforced jump process. Zbl 1364.60068Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 8 2017 External field QED on Cauchy surfaces for varying electromagnetic fields. Zbl 1350.81031Deckert, D.-A.; Merkl, F. 4 2016 A comparison of a nonlinear sigma model with general pinning and pinning at one point. Zbl 1336.60097Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 3 2016 Spontaneous breaking of rotational symmetry in the presence of defects. Zbl 1307.60142Heydenreich, Markus; Merkl, Franz; Rolles, Silke W. W. 7 2014 Dirac equation with external potential and initial data on Cauchy surfaces. Zbl 1303.81075Deckert, D.-A.; Merkl, F. 5 2014 Localization for a nonlinear sigma model in a strip related to vertex reinforced jump processes. Zbl 1307.82013Disertori, Margherita; Merkl, Franz; Rolles, Silke W. W. 4 2014 Computational aspects of modular forms and Galois representations. How one can compute in polynomial time the value of Ramanujan’s tau at a prime. Zbl 1216.11004 21 2011 Correlation inequalities for edge-reinforced random walk. Zbl 1243.60018Merkl, Franz; Rolles, Silke W. W. 1 2011 Time-evolution of the external field problem in quantum electrodynamics. Zbl 1314.81164Deckert, D.-A.; Dürr, D.; Merkl, F.; Schottenloher, M. 11 2010 Recurrence of edge-reinforced random walk on a two-dimensional graph. Zbl 1180.82085Merkl, Franz; Rolles, Silke W. W. 15 2009 Spontaneous breaking of continuous rotational symmetry in two dimensions. Zbl 1191.60115Merkl, Franz; Rolles, Silke W. W. 8 2009 Edge-reinforced random walk on one-dimensional periodic graphs. Zbl 1186.82039Merkl, Franz; Rolles, Silke W. W. 7 2009 Bounding a random environment bounding a random environment for two-dimensional edge-reinforced random walk. Zbl 1187.82051Merkl, Franz; Rolles, Silke W. W. 6 2008 The ’magic formula’ for linearly edge-reinforced random walks. Zbl 1146.60308Merkl, Franz; Öry, Aniko; Rolles, Silke W. W. 3 2008 A random environment for linearly edge-reinforced random walks on infinite graphs. Zbl 1116.60060Merkl, Franz; Rolles, Silke W. W. 8 2007 Asymptotic behavior of edge-reinforced random walks. Zbl 1206.82082Merkl, Franz; Rolles, Silke W. W. 6 2007 Linearly edge-reinforced random walks. Zbl 1125.82014Merkl, Franz; Rolles, Silke W. W. 12 2006 Edge-reinforced random walk on a ladder. Zbl 1102.82010Merkl, Franz; Rolles, Silke W. W. 9 2005 Reconstructing a multicolor random scenery seen along a random walk path with bounded jumps. Zbl 1064.60201Löwe, Matthias; Matzinger, Heinrich; Merkl, Franz 10 2004 Quenched asymptotics of the ground state energy of random Schrödinger operators with scaled Gibbsian potentials. Zbl 1106.82016Merkl, Franz 1 2003 Moderate deviations for longest increasing subsequences: The lower tail. Zbl 1011.60007Löwe, Matthias; Merkl, Franz; Rolles, Silke 13 2002 Infinite volume asymptotics of the ground state energy in a scaled Poissonian potential. Zbl 0996.82036Merkl, Franz; Wüthrich, Mario V. 5 2002 A zero-one law for planar random walks in random environment. Zbl 1016.60093Zerner, Martin P. W.; Merkl, Franz 19 2001 Moderate deviations for longest increasing subsequences: The upper tail. Zbl 1033.60035Löwe, Matthias; Merkl, Franz 15 2001 Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential. Zbl 1037.82022Merkl, Franz; Wüthrich, Mario V. 3 2001 Annealed survival asymptotics for Brownian motion in a scaled Poissonian potential. Zbl 1062.82022Merkl, Franz; Wüthrich, Mario V. 2 2001 Recurrent random walks and the absence of continuous symmetry breaking on graphs. Zbl 0828.60055Merkl, Franz; Wagner, Herbert 4 1994 all cited Publications top 5 cited Publications all top 5 Cited by 152 Authors 13 Merkl, Franz 12 Rolles, Silke W. W. 9 Sabot, Christophe 7 Tarrès, Pierre 6 Disertori, Margherita 6 Löwe, Matthias 5 Matzinger, Heinrich III 4 Basu, Riddhipratim 4 Deckert, Dirk-André 4 Tumulka, Roderich 3 Bauerschmidt, Roland 3 Berger, Noam 3 Collevecchio, Andrea 3 Drewitz, Alexander 3 Eichelsbacher, Peter 3 Kozma, Gady 3 Nickel, Lukas 3 Raimond, Olivier 3 Ramírez, Alejandro F. 3 Schapira, Bruno 3 Spencer, Thomas C. 3 Tournier, Laurent 3 Zeng, Xiaolin 2 Biskup, Marek 2 Crawford, Nicholas 2 Dereziński, Jan 2 Finster, Felix 2 Ganguly, Shirshendu 2 Hammond, Alan 2 Helmuth, Tyler 2 Holmes, Mark P. 2 König, Wolfgang Dieter 2 Kriecherbauer, Thomas 2 Lill, Sascha 2 Limic, Vlada 2 Richthammer, Thomas 2 Sarkar, Sourav 2 Sidoravicius, Vladas 2 Sly, Allan 2 Swan, Andrew W. 2 Takei, Masato 2 Theil, Florian 2 Zeitouni, Ofer 2 Zerner, Martin P. W. 1 Adams, Stefan 1 Akahori, Jirô 1 Angel, Omer 1 Antinucci, Giovanni 1 Astrauskas, Arvydas 1 Aumann, Simon 1 Bacallado, Sergio 1 Bachmat, Eitan 1 Barraquand, Guillaume 1 Benaïm, Michel 1 Benjamini, Itai 1 Blondel, Oriane 1 Bolthausen, Erwin 1 Bramson, Maury D. 1 Bruss, Franz Thomas 1 Chiaselotti, Giampiero 1 Chouk, Khalil 1 Comets, Francis M. 1 Conache, Diana 1 Corwin, Ivan Z. 1 Cotar, Codina 1 Delbaen, Freddy 1 den Hollander, Frank 1 Dereudre, David 1 Diehl, H. W. 1 Dimitrov, Evgeni I. 1 Drouilhet, Rémy 1 Dybalski, Wojciech 1 Engländer, János 1 Esfeld, Michael 1 Eyers, Michael 1 Favaro, Stefano 1 Finucane, Hilary K. 1 Foss, Sergey G. 1 Fresta, Luca 1 Gaál, Alexisz Tamás 1 Gairing, Jan M. 1 Gentile, Tommaso 1 Georgii, Hans-Otto 1 Gerard, Thomas 1 Giuliani, Alessandro 1 Goergen, Laurent 1 Gómez, Ricardo 1 Guo, Xiaoqin 1 Hart, Andrew G. 1 Hegde, Milind 1 Heydenreich, Markus 1 Hilário, Marcelo Richard 1 Hildebrand, Martin V. 1 Hirsch, Christian 1 Hoffman, Christopher 1 Hong, Wenming 1 Houdré, Christian 1 Infusino, Federico G. 1 Jalowy, Jonas 1 Kannan, Devika ...and 52 more Authors all top 5 Cited in 44 Serials 17 The Annals of Probability 14 Probability Theory and Related Fields 11 Stochastic Processes and their Applications 9 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 8 Communications in Mathematical Physics 6 Journal of Mathematical Physics 6 Journal of Statistical Physics 6 Annales Henri Poincaré 4 Electronic Journal of Probability 4 Electronic Communications in Probability 3 Letters in Mathematical Physics 3 Journal of Theoretical Probability 3 The Annals of Applied Probability 2 Israel Journal of Mathematics 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 International Journal of Modern Physics B 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Theoretical and Mathematical Physics 1 The Annals of Statistics 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Applied Probability 1 Journal of Multivariate Analysis 1 Statistics & Probability Letters 1 Stochastic Analysis and Applications 1 Acta Mathematicae Applicatae Sinica. English Series 1 Algorithmica 1 Journal of the American Mathematical Society 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Bernoulli 1 ELA. The Electronic Journal of Linear Algebra 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Journal of High Energy Physics 1 Brazilian Journal of Probability and Statistics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Bulletin of the Brazilian Mathematical Society. New Series 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Science China. Mathematics 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Quanta all top 5 Cited in 25 Fields 102 Probability theory and stochastic processes (60-XX) 52 Statistical mechanics, structure of matter (82-XX) 30 Quantum theory (81-XX) 9 Combinatorics (05-XX) 7 Partial differential equations (35-XX) 3 Mechanics of deformable solids (74-XX) 3 Relativity and gravitational theory (83-XX) 2 Group theory and generalizations (20-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year