Xue, Ling; Zhang, Min; Zhao, Kun; Zheng, Xiaoming Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks. (English) Zbl 07634552 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106913, 14 p. (2023). MSC: 35Q92 35B35 PDF BibTeX XML Cite \textit{L. Xue} et al., Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106913, 14 p. (2023; Zbl 07634552) Full Text: DOI OpenURL
Erhard, Dirk; Franco, Tertuliano; Reis, Guilherme The directed edge reinforced random walk: the Ant Mill phenomenon. (English) Zbl 07625675 J. Stat. Phys. 190, No. 1, Paper No. 18, 18 p. (2023). MSC: 60K35 60K37 60G50 PDF BibTeX XML Cite \textit{D. Erhard} et al., J. Stat. Phys. 190, No. 1, Paper No. 18, 18 p. (2023; Zbl 07625675) Full Text: DOI arXiv OpenURL
Bertenghi, Marco; Rosales-Ortiz, Alejandro Joint invariance principles for random walks with positively and negatively reinforced steps. (English) Zbl 07596214 J. Stat. Phys. 189, No. 3, Paper No. 35, 31 p. (2022). MSC: 60G50 60G51 60K35 PDF BibTeX XML Cite \textit{M. Bertenghi} and \textit{A. Rosales-Ortiz}, J. Stat. Phys. 189, No. 3, Paper No. 35, 31 p. (2022; Zbl 07596214) Full Text: DOI arXiv OpenURL
Rosales, Rafael A.; Prado, Fernando P. A.; Pires, Benito Vertex reinforced random walks with exponential interaction on complete graphs. (English) Zbl 1492.60289 Stochastic Processes Appl. 148, 353-379 (2022). MSC: 60K35 37C10 60J10 60G50 PDF BibTeX XML Cite \textit{R. A. Rosales} et al., Stochastic Processes Appl. 148, 353--379 (2022; Zbl 1492.60289) Full Text: DOI arXiv OpenURL
Laulin, Lucile New insights on the reinforced elephant random walk using a martingale approach. (English) Zbl 1490.60108 J. Stat. Phys. 186, No. 1, Paper No. 9, 23 p. (2022). MSC: 60G50 60G42 60F17 PDF BibTeX XML Cite \textit{L. Laulin}, J. Stat. Phys. 186, No. 1, Paper No. 9, 23 p. (2022; Zbl 1490.60108) Full Text: DOI arXiv OpenURL
Kious, Daniel; Schapira, Bruno; Singh, Arvind Once reinforced random walk on \(\mathbb{Z}\times\gamma\). (English. French summary) Zbl 1487.60188 Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 4, 2219-2242 (2021). MSC: 60K35 60G50 60K37 PDF BibTeX XML Cite \textit{D. Kious} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 4, 2219--2242 (2021; Zbl 1487.60188) Full Text: DOI arXiv OpenURL
Huang, Xiangyu; Liu, Yong; Sidoravicius, Vladas; Xiang, Kainan A note on once reinforced random walk on ladder \(\mathbb{Z} \times \{0, 1 \} \). (English) Zbl 1483.60147 Electron. Commun. Probab. 26, Paper No. 38, 12 p. (2021). MSC: 60K35 PDF BibTeX XML Cite \textit{X. Huang} et al., Electron. Commun. Probab. 26, Paper No. 38, 12 p. (2021; Zbl 1483.60147) Full Text: DOI OpenURL
Schapira, Bruno Localization on 5 sites for vertex reinforced random walks: towards a characterization. (English) Zbl 1479.60202 Ann. Appl. Probab. 31, No. 4, 1774-1786 (2021). MSC: 60K35 60G50 PDF BibTeX XML Cite \textit{B. Schapira}, Ann. Appl. Probab. 31, No. 4, 1774--1786 (2021; Zbl 1479.60202) Full Text: DOI arXiv Link OpenURL
Fribergh, Alexander; Kious, Daniel; Sidoravicius, Vladas; Stauffer, Alexandre Random memory walk. (English) Zbl 1469.60327 Vares, Maria Eulália (ed.) et al., In and out of equilibrium 3: celebrating Vladas Sidoravicius. Cham: Birkhäuser. Prog. Probab. 77, 439-453 (2021). MSC: 60K35 PDF BibTeX XML Cite \textit{A. Fribergh} et al., Prog. Probab. 77, 439--453 (2021; Zbl 1469.60327) Full Text: DOI arXiv OpenURL
Kozma, Gady; Peled, Ron Power-law decay of weights and recurrence of the two-dimensional VRJP. (English) Zbl 1478.60265 Electron. J. Probab. 26, Paper No. 82, 19 p. (2021). MSC: 60K35 60K37 81T25 81T60 PDF BibTeX XML Cite \textit{G. Kozma} and \textit{R. Peled}, Electron. J. Probab. 26, Paper No. 82, 19 p. (2021; Zbl 1478.60265) Full Text: DOI arXiv OpenURL
Dinh, Thu; Xin, Jack Enhanced diffusivity in perturbed senile reinforced random walk models. (English) Zbl 1472.35291 Asymptotic Anal. 122, No. 1-2, 87-104 (2021). MSC: 35Q35 76F99 82C41 82C31 60G50 60K35 PDF BibTeX XML Cite \textit{T. Dinh} and \textit{J. Xin}, Asymptotic Anal. 122, No. 1--2, 87--104 (2021; Zbl 1472.35291) Full Text: DOI arXiv OpenURL
Fasino, Dario; Tudisco, Francesco Ergodicity coefficients for higher-order stochastic processes. (English) Zbl 1483.60105 SIAM J. Math. Data Sci. 2, No. 3, 740-769 (2020). MSC: 60J10 60G50 65C30 65F35 65C40 PDF BibTeX XML Cite \textit{D. Fasino} and \textit{F. Tudisco}, SIAM J. Math. Data Sci. 2, No. 3, 740--769 (2020; Zbl 1483.60105) Full Text: DOI arXiv OpenURL
Bonilla, Luis L.; Carretero, Manuel; Terragni, Filippo Integrodifference master equation describing actively growing blood vessels in angiogenesis. (English) Zbl 07446864 Int. J. Nonlinear Sci. Numer. Simul. 21, No. 7-8, 705-713 (2020). MSC: 92-XX 60-XX PDF BibTeX XML Cite \textit{L. L. Bonilla} et al., Int. J. Nonlinear Sci. Numer. Simul. 21, No. 7--8, 705--713 (2020; Zbl 07446864) Full Text: DOI arXiv Link OpenURL
Holmes, Mark; Kious, Daniel A monotonicity property for once reinforced biased random walk on \(\mathbb{Z}^d\). (English) Zbl 1446.82030 Sidoravicius, Vladas (ed.), Sojourns in probability theory and statistical physics. III. Interacting particle systems and random walks, a festschrift for Charles M. Newman. Singapore: Springer; Shanghai: NYU Shanghai. Springer Proc. Math. Stat. 300, 255-273 (2019). MSC: 82B41 60J80 60J50 60K37 PDF BibTeX XML Cite \textit{M. Holmes} and \textit{D. Kious}, Springer Proc. Math. Stat. 300, 255--273 (2019; Zbl 1446.82030) Full Text: DOI OpenURL
Bonilla, Luis L.; Carretero, Manuel; Terragni, Filippo Stochastic models of blood vessel growth. (English) Zbl 1442.82009 Giacomin, Giambattista (ed.) et al., Stochastic dynamics out of equilibrium. Lecture notes from the IHP trimester, Institut Henri Poincaré (IHP), Paris, France, April – July, 2017. Cham: Springer. Springer Proc. Math. Stat. 282, 413-436 (2019). MSC: 82C20 82C41 82C31 60H10 60H15 34F05 92C15 92C17 35R09 PDF BibTeX XML Cite \textit{L. L. Bonilla} et al., Springer Proc. Math. Stat. 282, 413--436 (2019; Zbl 1442.82009) Full Text: DOI OpenURL
Serlet, Laurent Explicit laws for the records of the perturbed random walk on \(\mathbb{Z} \). (English) Zbl 1452.60029 Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLIX. Cham: Springer. Lect. Notes Math. 2215, 495-519 (2018). MSC: 60G50 60F17 60J10 PDF BibTeX XML Cite \textit{L. Serlet}, Lect. Notes Math. 2215, 495--519 (2018; Zbl 1452.60029) Full Text: DOI OpenURL
Collevecchio, Andrea; Holmes, Mark; Kious, Daniel On the speed of once-reinforced biased random walk on trees. (English) Zbl 1417.60085 Electron. J. Probab. 23, Paper No. 86, 32 p. (2018). MSC: 60K37 60G50 60J80 PDF BibTeX XML Cite \textit{A. Collevecchio} et al., Electron. J. Probab. 23, Paper No. 86, 32 p. (2018; Zbl 1417.60085) Full Text: DOI arXiv Euclid OpenURL
Chen, Xinxin; Zeng, Xiaolin Speed of vertex-reinforced jump process on Galton-Watson trees. (English) Zbl 1429.60067 J. Theor. Probab. 31, No. 2, 1166-1211 (2018). MSC: 60J80 60K37 PDF BibTeX XML Cite \textit{X. Chen} and \textit{X. Zeng}, J. Theor. Probab. 31, No. 2, 1166--1211 (2018; Zbl 1429.60067) Full Text: DOI arXiv OpenURL
Kious, Daniel; Sidoravicius, Vladas Phase transition for the once-reinforced random walk on \(\mathbb{Z}^{d}\)-like trees. (English) Zbl 1429.60074 Ann. Probab. 46, No. 4, 2121-2133 (2018). MSC: 60K35 PDF BibTeX XML Cite \textit{D. Kious} and \textit{V. Sidoravicius}, Ann. Probab. 46, No. 4, 2121--2133 (2018; Zbl 1429.60074) Full Text: DOI arXiv Euclid OpenURL
Le Goff, Line C.; Raimond, Olivier Vertex reinforced non-backtracking random walks: an example of path formation. (English) Zbl 1430.60086 Electron. J. Probab. 23, Paper No. 39, 38 p. (2018). MSC: 60K35 60G99 91C99 PDF BibTeX XML Cite \textit{L. C. Le Goff} and \textit{O. Raimond}, Electron. J. Probab. 23, Paper No. 39, 38 p. (2018; Zbl 1430.60086) Full Text: DOI arXiv Euclid OpenURL
Cénac, Peggy; Le Ny, Arnaud; de Loynes, Basile; Offret, Yoann Persistent random walks. I. Recurrence versus transience. (English) Zbl 1390.60165 J. Theor. Probab. 31, No. 1, 232-243 (2018). MSC: 60G50 60G17 60J05 37B20 60K35 PDF BibTeX XML Cite \textit{P. Cénac} et al., J. Theor. Probab. 31, No. 1, 232--243 (2018; Zbl 1390.60165) Full Text: DOI Link OpenURL
Sabot, Christophe; Tarrès, Pierre; Zeng, Xiaolin The vertex reinforced jump process and a random Schrödinger operator on finite graphs. (English) Zbl 06838112 Ann. Probab. 45, No. 6A, 3967-3986 (2017). MSC: 60K37 60K35 82B44 81T25 81T60 PDF BibTeX XML Cite \textit{C. Sabot} et al., Ann. Probab. 45, No. 6A, 3967--3986 (2017; Zbl 06838112) Full Text: DOI arXiv Euclid OpenURL
Cotar, Codina; Thacker, Debleena Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs. (English) Zbl 1418.60036 Ann. Probab. 45, No. 4, 2655-2706 (2017). MSC: 60G50 60J10 60K35 PDF BibTeX XML Cite \textit{C. Cotar} and \textit{D. Thacker}, Ann. Probab. 45, No. 4, 2655--2706 (2017; Zbl 1418.60036) Full Text: DOI arXiv Euclid OpenURL
Benson, Austin R.; Gleich, David F.; Lim, Lek-Heng The spacey random walk: a stochastic process for higher-order data. (English) Zbl 1365.15033 SIAM Rev. 59, No. 2, 321-345 (2017). MSC: 15A69 65C50 60G50 60J10 15B51 15A18 PDF BibTeX XML Cite \textit{A. R. Benson} et al., SIAM Rev. 59, No. 2, 321--345 (2017; Zbl 1365.15033) Full Text: DOI arXiv OpenURL
Bacallado, Sergio; Pande, Vijay; Favaro, Stefano; Trippa, Lorenzo Bayesian regularization of the length of memory in reversible sequences. (English) Zbl 1414.62084 J. R. Stat. Soc., Ser. B, Stat. Methodol. 78, No. 4, 933-946 (2016). MSC: 62F15 60J10 62M05 PDF BibTeX XML Cite \textit{S. Bacallado} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 78, No. 4, 933--946 (2016; Zbl 1414.62084) Full Text: DOI Link OpenURL
Sabot, Christophe; Tarrès, Pierre Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model. (English) Zbl 1331.60185 J. Eur. Math. Soc. (JEMS) 17, No. 9, 2353-2378 (2015). Reviewer: Marius Iosifescu (Bucureşti) MSC: 60K37 60G50 60K35 60J75 81T25 81T60 PDF BibTeX XML Cite \textit{C. Sabot} and \textit{P. Tarrès}, J. Eur. Math. Soc. (JEMS) 17, No. 9, 2353--2378 (2015; Zbl 1331.60185) Full Text: DOI arXiv OpenURL
Disertori, Margherita; Sabot, Christophe; Tarrès, Pierre Transience of edge-reinforced random walk. (English) Zbl 1329.60116 Commun. Math. Phys. 339, No. 1, 121-148 (2015). Reviewer: Martynas Manstavičius (Vilnius) MSC: 60G50 60J75 60K37 60K35 05C81 PDF BibTeX XML Cite \textit{M. Disertori} et al., Commun. Math. Phys. 339, No. 1, 121--148 (2015; Zbl 1329.60116) Full Text: DOI arXiv OpenURL
Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas Monotone interaction of walk and graph: recurrence versus transience. (English) Zbl 1307.60140 Electron. Commun. Probab. 19, Paper No. 76, 12 p. (2014). MSC: 60K35 60G50 82C41 PDF BibTeX XML Cite \textit{A. Dembo} et al., Electron. Commun. Probab. 19, Paper No. 76, 12 p. (2014; Zbl 1307.60140) Full Text: DOI arXiv OpenURL
Chen, Jun Two particles’ repelling random walks on the complete graph. (English) Zbl 1307.60048 Electron. J. Probab. 19, Paper No. 113, 17 p. (2014). MSC: 60G50 60K35 05C81 37C10 PDF BibTeX XML Cite \textit{J. Chen}, Electron. J. Probab. 19, Paper No. 113, 17 p. (2014; Zbl 1307.60048) Full Text: DOI OpenURL
Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas Walking within growing domains: recurrence versus transience. (English) Zbl 1307.60149 Electron. J. Probab. 19, Paper No. 106, 20 p. (2014). MSC: 60K37 60K35 82C24 PDF BibTeX XML Cite \textit{A. Dembo} et al., Electron. J. Probab. 19, Paper No. 106, 20 p. (2014; Zbl 1307.60149) Full Text: DOI arXiv OpenURL
Chen, Jun; Kozma, Gady Vertex-reinforced random walk on \(\mathbb Z\) with sub-square-root weights is recurrent. (Récurrence d’une marche aléatoire renforcée par sommets sur \(\mathbb Z\) avec poids inférieur à racine carrée.) (English. French summary) Zbl 1307.60049 C. R., Math., Acad. Sci. Paris 352, No. 6, 521-524 (2014). Reviewer: Boris Granovsky (Haifa) MSC: 60G50 60J27 60J28 60F20 PDF BibTeX XML Cite \textit{J. Chen} and \textit{G. Kozma}, C. R., Math., Acad. Sci. Paris 352, No. 6, 521--524 (2014; Zbl 1307.60049) Full Text: DOI arXiv Link OpenURL
Percus, Jerome K.; Percus, Ora E. Reinforced Brownian motion: a prototype. (English) Zbl 1302.82054 J. Stat. Phys. 156, No. 5, 917-931 (2014). MSC: 82B41 60J65 PDF BibTeX XML Cite \textit{J. K. Percus} and \textit{O. E. Percus}, J. Stat. Phys. 156, No. 5, 917--931 (2014; Zbl 1302.82054) Full Text: DOI arXiv OpenURL
Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind Localization on 4 sites for vertex-reinforced random walks on \(\mathbb{Z}\). (English) Zbl 1297.60062 Ann. Probab. 42, No. 2, 527-558 (2014). Reviewer: Chen Mu-Fa (Beijing) MSC: 60K35 60G50 60J20 PDF BibTeX XML Cite \textit{A.-L. Basdevant} et al., Ann. Probab. 42, No. 2, 527--558 (2014; Zbl 1297.60062) Full Text: DOI arXiv Euclid OpenURL
Kozma, Gady Reinforced random walk. (English) Zbl 1364.60135 Latała, Rafał (ed.) et al., European Congress of Mathematics. Proceedings of the 6th ECM congress, Kraków, Poland, July 2–7 July, 2012. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-120-0/hbk). 429-443 (2013). MSC: 60K35 60K37 60G50 60G09 60J10 PDF BibTeX XML Cite \textit{G. Kozma}, in: European Congress of Mathematics. Proceedings of the 6th ECM congress, Kraków, Poland, July 2--7 July, 2012. Zürich: European Mathematical Society (EMS). 429--443 (2013; Zbl 1364.60135) Full Text: DOI arXiv OpenURL
Horger, Thomas; Oelker, Aenne; Kuttler, Christina; Pérez-Velázquez, Judith Mathematical modeling of tumor-induced angiogenesis using porous medium diffusion. (English) Zbl 1331.92023 Int. J. Biomath. Biostat. 2, No. 2, 145-165 (2013). MSC: 92C15 92C50 35Q92 PDF BibTeX XML Cite \textit{T. Horger} et al., Int. J. Biomath. Biostat. 2, No. 2, 145--165 (2013; Zbl 1331.92023) OpenURL
Rao, K. Balaji; Anoop, M. B. Why do we need probability distributions with fat tails to describe the surface strain evolution in reinforced concrete flexural members? (English) Zbl 1293.74434 Meccanica 48, No. 6, 1517-1542 (2013). MSC: 74S60 74E30 PDF BibTeX XML Cite \textit{K. B. Rao} and \textit{M. B. Anoop}, Meccanica 48, No. 6, 1517--1542 (2013; Zbl 1293.74434) Full Text: DOI OpenURL
Budhiraja, Amarjit; Del Moral, Pierre; Rubenthaler, Sylvain Discrete time Markovian agents interacting through a potential. (English) Zbl 1374.60126 ESAIM, Probab. Stat. 17, 614-634 (2013). MSC: 60J05 60K35 92C45 70K20 60K40 PDF BibTeX XML Cite \textit{A. Budhiraja} et al., ESAIM, Probab. Stat. 17, 614--634 (2013; Zbl 1374.60126) Full Text: DOI arXiv OpenURL
Bouchet, Élodie Sub-ballistic random walk in Dirichlet environment. (English) Zbl 1296.60267 Electron. J. Probab. 18, Paper No. 58, 25 p. (2013). MSC: 60K37 60K35 PDF BibTeX XML Cite \textit{É. Bouchet}, Electron. J. Probab. 18, Paper No. 58, 25 p. (2013; Zbl 1296.60267) Full Text: DOI arXiv OpenURL
Benaim, Michel; Raimond, Olivier; Schapira, Bruno Strongly vertex-reinforced-random-walk on a complete graph. (English) Zbl 1277.60169 ALEA, Lat. Am. J. Probab. Math. Stat. 10, No. 2, 767-782 (2013). MSC: 60K35 PDF BibTeX XML Cite \textit{M. Benaim} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 10, No. 2, 767--782 (2013; Zbl 1277.60169) Full Text: arXiv Link OpenURL
Sabot, Christophe Random Dirichlet environment viewed from the particle in dimension \(d\geq 3\). (English) Zbl 1269.60077 Ann. Probab. 41, No. 2, 722-743 (2013). MSC: 60K37 60K35 PDF BibTeX XML Cite \textit{C. Sabot}, Ann. Probab. 41, No. 2, 722--743 (2013; Zbl 1269.60077) Full Text: DOI arXiv Euclid OpenURL
Serlet, Laurent Hitting times for the perturbed reflecting random walk. (English) Zbl 1259.82045 Stochastic Processes Appl. 123, No. 1, 110-130 (2013). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B41 60J65 PDF BibTeX XML Cite \textit{L. Serlet}, Stochastic Processes Appl. 123, No. 1, 110--130 (2013; Zbl 1259.82045) Full Text: DOI OpenURL
Schapira, Bruno A 0-1 law for vertex-reinforced random walks on \(\mathbb{Z}\) with weight of order \(k^\alpha,\;\alpha\in[0,1/2)\). (English) Zbl 1244.60033 Electron. Commun. Probab. 17, Paper No. 22, 8 p. (2012). MSC: 60F20 60K35 PDF BibTeX XML Cite \textit{B. Schapira}, Electron. Commun. Probab. 17, Paper No. 22, 8 p. (2012; Zbl 1244.60033) Full Text: DOI arXiv OpenURL
van der Hofstad, Remco; Holmes, Mark An expansion for self-interacting random walks. (English) Zbl 1238.60116 Braz. J. Probab. Stat. 26, No. 1, 1-55 (2012). Reviewer: Stella Kapodistria (Eindhoven) MSC: 60K37 82B41 60G50 PDF BibTeX XML Cite \textit{R. van der Hofstad} and \textit{M. Holmes}, Braz. J. Probab. Stat. 26, No. 1, 1--55 (2012; Zbl 1238.60116) Full Text: DOI arXiv OpenURL
Merkl, Franz; Rolles, Silke W. W. Correlation inequalities for edge-reinforced random walk. (English) Zbl 1243.60018 Electron. Commun. Probab. 16, 753-763 (2011). MSC: 60E15 82B41 60K35 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Electron. Commun. Probab. 16, 753--763 (2011; Zbl 1243.60018) Full Text: DOI OpenURL
Collevecchio, Andrea; Schmitz, Tom Bounds on the speed and on regeneration times for certain processes on regular trees. (English) Zbl 1225.60156 Ann. Appl. Probab. 21, No. 3, 1073-1101 (2011). Reviewer: Dominique Lepingle (Orléans) MSC: 60K37 60K99 PDF BibTeX XML Cite \textit{A. Collevecchio} and \textit{T. Schmitz}, Ann. Appl. Probab. 21, No. 3, 1073--1101 (2011; Zbl 1225.60156) Full Text: DOI arXiv OpenURL
Cohen, Netta; Jordan, Jonathan; Voliotis, Margaritis Preferential duplication graphs. (English) Zbl 1216.05142 J. Appl. Probab. 47, No. 2, 572-585 (2010). Reviewer: David B. Penman (Colchester) MSC: 05C80 60G99 60K35 PDF BibTeX XML Cite \textit{N. Cohen} et al., J. Appl. Probab. 47, No. 2, 572--585 (2010; Zbl 1216.05142) Full Text: DOI OpenURL
Cotar, Codina; Limic, Vlada Attraction time for strongly reinforced walks. (English) Zbl 1213.60087 Ann. Appl. Probab. 19, No. 5, 1972-2007 (2009). Reviewer: Alexander V. Bulinski (Moskva) MSC: 60G50 60J10 60K35 PDF BibTeX XML Cite \textit{C. Cotar} and \textit{V. Limic}, Ann. Appl. Probab. 19, No. 5, 1972--2007 (2009; Zbl 1213.60087) Full Text: DOI arXiv OpenURL
Merkl, Franz; Rolles, Silke W. W. Recurrence of edge-reinforced random walk on a two-dimensional graph. (English) Zbl 1180.82085 Ann. Probab. 37, No. 5, 1679-1714 (2009). Reviewer: Guy Jumarie (Montréal) MSC: 82B41 60K35 60K37 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Ann. Probab. 37, No. 5, 1679--1714 (2009; Zbl 1180.82085) Full Text: DOI arXiv OpenURL
Merkl, Franz; Rolles, Silke W. W. Edge-reinforced random walk on one-dimensional periodic graphs. (English) Zbl 1186.82039 Probab. Theory Relat. Fields 145, No. 3-4, 323-349 (2009). Reviewer: Achim Klenke (Mainz) MSC: 82B41 60K35 60K37 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Probab. Theory Relat. Fields 145, No. 3--4, 323--349 (2009; Zbl 1186.82039) Full Text: DOI OpenURL
Merkl, Franz; Rolles, Silke W. W. Bounding a random environment bounding a random environment for two-dimensional edge-reinforced random walk. (English) Zbl 1187.82051 Electron. J. Probab. 13, 530-565 (2008). MSC: 82B41 60K35 60K37 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Electron. J. Probab. 13, 530--565 (2008; Zbl 1187.82051) Full Text: DOI EuDML EMIS OpenURL
Takei, Masato; Takeshima, Masaki Phase diagram for once-reinforced random walks on trees with exponential weighting scheme. (English) Zbl 1202.60068 Stat. Probab. Lett. 78, No. 17, 3000-3007 (2008). Reviewer: Wolfgang König (Leipzig) MSC: 60G50 60K35 PDF BibTeX XML Cite \textit{M. Takei} and \textit{M. Takeshima}, Stat. Probab. Lett. 78, No. 17, 3000--3007 (2008; Zbl 1202.60068) Full Text: DOI OpenURL
Myjak, Józef; Rudnicki, Ryszard Reinforced walk on graphs and neural networks. (English) Zbl 1154.60360 Stud. Math. 189, No. 3, 255-268 (2008). MSC: 60K37 60J10 60J20 60G50 82C41 PDF BibTeX XML Cite \textit{J. Myjak} and \textit{R. Rudnicki}, Stud. Math. 189, No. 3, 255--268 (2008; Zbl 1154.60360) Full Text: DOI OpenURL
Sellke, T. Reinforced random walk on the \(d\)-dimensional integer lattice. (English) Zbl 1154.82011 Markov Process. Relat. Fields 14, No. 2, 291-308 (2008). Reviewer: Achim Klenke (Mainz) MSC: 82B41 60K35 PDF BibTeX XML Cite \textit{T. Sellke}, Markov Process. Relat. Fields 14, No. 2, 291--308 (2008; Zbl 1154.82011) OpenURL
Aidékon, Elie Transient random walks in random environment on a Galton-Watson tree. (English) Zbl 1146.60078 Probab. Theory Relat. Fields 142, No. 3-4, 525-559 (2008). MSC: 60K37 60J80 60F15 PDF BibTeX XML Cite \textit{E. Aidékon}, Probab. Theory Relat. Fields 142, No. 3--4, 525--559 (2008; Zbl 1146.60078) Full Text: DOI arXiv OpenURL
Kovchegov, Yevgeniy Multi-particle processes with reinforcements. (English) Zbl 1141.60071 J. Theor. Probab. 21, No. 2, 437-448 (2008). MSC: 60K37 60C05 60G07 60G09 PDF BibTeX XML Cite \textit{Y. Kovchegov}, J. Theor. Probab. 21, No. 2, 437--448 (2008; Zbl 1141.60071) Full Text: DOI arXiv OpenURL
Pemantle, Robin A survey of random processes with reinforcement. (English) Zbl 1189.60138 Probab. Surv. 4, 1-79 (2007). MSC: 60J20 60G50 37A50 60K40 60-02 PDF BibTeX XML Cite \textit{R. Pemantle}, Probab. Surv. 4, 1--79 (2007; Zbl 1189.60138) Full Text: DOI arXiv EuDML OpenURL
Limic, Vlada; Tarrès, Pierre Attracting edge and strongly edge reinforced walks. (English) Zbl 1131.60036 Ann. Probab. 35, No. 5, 1783-1806 (2007). Reviewer: Alexander V. Bulinskij (Moskva) MSC: 60G50 60J10 60K35 PDF BibTeX XML Cite \textit{V. Limic} and \textit{P. Tarrès}, Ann. Probab. 35, No. 5, 1783--1806 (2007; Zbl 1131.60036) Full Text: DOI arXiv OpenURL
Merkl, Franz; Rolles, Silke W. W. A random environment for linearly edge-reinforced random walks on infinite graphs. (English) Zbl 1116.60060 Probab. Theory Relat. Fields 138, No. 1-2, 157-176 (2007). MSC: 60K37 60K35 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Probab. Theory Relat. Fields 138, No. 1--2, 157--176 (2007; Zbl 1116.60060) Full Text: DOI Link OpenURL
Merkl, Franz; Rolles, Silke W. W. Linearly edge-reinforced random walks. (English) Zbl 1125.82014 Denteneer, Dee (ed.) et al., Dynamics and stochastics. Festschrift in honor of M. S. Keane. Selected papers based on the presentations at the conference ‘Dynamical systems, probability theory, and statistical mechanics’, Eindhoven, The Netherlands, January 3–7, 2005, on the occasion of the 65th birthday of Mike S. Keane. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-64-1/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 48, 66-77 (2006). MSC: 82B41 60K35 60K37 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, IMS Lect. Notes, Monogr. Ser. 48, 66--77 (2006; Zbl 1125.82014) Full Text: DOI arXiv Link OpenURL
Collevecchio, Andrea On the transience of processes defined on Galton-Watson trees. (English) Zbl 1104.60048 Ann. Probab. 34, No. 3, 870-878 (2006). MSC: 60J80 60G50 60J75 PDF BibTeX XML Cite \textit{A. Collevecchio}, Ann. Probab. 34, No. 3, 870--878 (2006; Zbl 1104.60048) Full Text: DOI arXiv OpenURL
Merkl, Franz; Rolles, Silke W. W. Edge-reinforced random walk on a ladder. (English) Zbl 1102.82010 Ann. Probab. 33, No. 6, 2051-2093 (2005). Reviewer: Utkir Rozikov (Tashkent) MSC: 82B41 60K35 60K37 PDF BibTeX XML Cite \textit{F. Merkl} and \textit{S. W. W. Rolles}, Ann. Probab. 33, No. 6, 2051--2093 (2005; Zbl 1102.82010) Full Text: DOI arXiv OpenURL
Sabot, Christophe Markov chains in a Dirichlet environment and hypergeometric integrals. (English) Zbl 1087.60078 C. R., Math., Acad. Sci. Paris 342, No. 1, 57-62 (2005). Reviewer: Yuri Kozitsky (Lublin) MSC: 60K37 82D30 PDF BibTeX XML Cite \textit{C. Sabot}, C. R., Math., Acad. Sci. Paris 342, No. 1, 57--62 (2005; Zbl 1087.60078) Full Text: DOI arXiv OpenURL
Dai, Jack Jie Some results regarding vertex-reinforced random walks. (English) Zbl 1102.60040 Stat. Probab. Lett. 66, No. 3, 259-266 (2004). MSC: 60G50 PDF BibTeX XML Cite \textit{J. J. Dai}, Stat. Probab. Lett. 66, No. 3, 259--266 (2004; Zbl 1102.60040) Full Text: DOI OpenURL
Volkov, Stanislav Excited random walk on trees. (English) Zbl 1065.60097 Electron. J. Probab. 8, Paper No. 23, 15 p. (2003). MSC: 60J10 60G50 PDF BibTeX XML Cite \textit{S. Volkov}, Electron. J. Probab. 8, Paper No. 23, 15 p. (2003; Zbl 1065.60097) Full Text: DOI EuDML EMIS OpenURL
Limic, Vlada Attracting edge property for a class of reinforced random walks. (English) Zbl 1057.60048 Ann. Probab. 31, No. 3, 1615-1654 (2003). Reviewer: Wolfgang König (Leipzig) MSC: 60G50 PDF BibTeX XML Cite \textit{V. Limic}, Ann. Probab. 31, No. 3, 1615--1654 (2003; Zbl 1057.60048) Full Text: DOI Euclid OpenURL
Plank, M. J.; Sleeman, B. D. A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. (English) Zbl 1044.92036 Math. Med. Biol. 20, No. 2, 135-181 (2003). MSC: 92C50 60G50 35Q92 PDF BibTeX XML Cite \textit{M. J. Plank} and \textit{B. D. Sleeman}, Math. Med. Biol. 20, No. 2, 135--181 (2003; Zbl 1044.92036) Full Text: DOI OpenURL
Dai, Jack Jie A note on vertex-reinforced random walks. (English) Zbl 1116.60331 Stat. Probab. Lett. 62, No. 3, 275-280 (2003). MSC: 60G50 60G42 PDF BibTeX XML Cite \textit{J. J. Dai}, Stat. Probab. Lett. 62, No. 3, 275--280 (2003; Zbl 1116.60331) Full Text: DOI OpenURL
Rolles, Silke W. W. How edge-reinforced random walk arises naturally. (English) Zbl 1029.60089 Probab. Theory Relat. Fields 126, No. 2, 243-260 (2003). Reviewer: A.Pellegrinotti (Roma) MSC: 60K37 60G09 PDF BibTeX XML Cite \textit{S. W. W. Rolles}, Probab. Theory Relat. Fields 126, No. 2, 243--260 (2003; Zbl 1029.60089) Full Text: DOI OpenURL
Plank, M. J.; Sleeman, B. D.; Jones, P. F. A mathematical model of an In Vitro experiment to investigate endothelial cell migration. (English) Zbl 1052.92022 J. Theor. Med. 4, No. 4, 251-270 (2002). MSC: 92C37 92C50 60G50 92C17 60G35 PDF BibTeX XML Cite \textit{M. J. Plank} et al., J. Theor. Med. 4, No. 4, 251--270 (2002; Zbl 1052.92022) Full Text: DOI EuDML OpenURL
Keane, M. S.; Rolles, S. W. W. Tubular recurrence. (English) Zbl 1026.60089 Acta Math. Hung. 97, No. 3, 207-221 (2002). Reviewer: S.K.Srinivasan (Chennai) MSC: 60J10 05C99 60K37 PDF BibTeX XML Cite \textit{M. S. Keane} and \textit{S. W. W. Rolles}, Acta Math. Hung. 97, No. 3, 207--221 (2002; Zbl 1026.60089) Full Text: DOI OpenURL
Durrett, Rick; Kesten, Harry; Limic, Vlada Once edge-reinforced random walk on a tree. (English) Zbl 0995.60042 Probab. Theory Relat. Fields 122, No. 4, 567-592 (2002). MSC: 60G50 60K99 PDF BibTeX XML Cite \textit{R. Durrett} et al., Probab. Theory Relat. Fields 122, No. 4, 567--592 (2002; Zbl 0995.60042) Full Text: DOI OpenURL
Volkov, Stanislav Vertex-reinforced random walk on arbitrary graphs. (English) Zbl 1031.60089 Ann. Probab. 29, No. 1, 66-91 (2001). Reviewer: Nina Gantert (Karlsruhe) MSC: 60K37 60G50 PDF BibTeX XML Cite \textit{S. Volkov}, Ann. Probab. 29, No. 1, 66--91 (2001; Zbl 1031.60089) Full Text: DOI arXiv OpenURL
Takeshima, Masaki Estimates of hitting probabilities for a 1-dimensional reinforced random walk. (English) Zbl 0992.60071 Osaka J. Math. 38, No. 4, 693-709 (2001). Reviewer: Thomas Simon (Évry) MSC: 60J10 PDF BibTeX XML Cite \textit{M. Takeshima}, Osaka J. Math. 38, No. 4, 693--709 (2001; Zbl 0992.60071) OpenURL
Takeshima, Masaki Behavior of 1-dimensional reinforced random walk. (English) Zbl 0962.60017 Osaka J. Math. 37, No. 2, 355-372 (2000). Reviewer: Gheorghe Oprişan (Bucureşti) MSC: 60G50 60J10 60F05 PDF BibTeX XML Cite \textit{M. Takeshima}, Osaka J. Math. 37, No. 2, 355--372 (2000; Zbl 0962.60017) OpenURL
Rudnicki, Ryszard; Wolf, Marek Random walk with memory. (English) Zbl 0953.60080 J. Math. Phys. 40, No. 6, 3072-3083 (1999). Reviewer: G.Oprişan (Bucureşti) MSC: 60J99 60J10 PDF BibTeX XML Cite \textit{R. Rudnicki} and \textit{M. Wolf}, J. Math. Phys. 40, No. 6, 3072--3083 (1999; Zbl 0953.60080) Full Text: DOI Link OpenURL
Davis, Burgess Brownian motion and random walk perturbed at extrema. (English) Zbl 0930.60041 Probab. Theory Relat. Fields 113, No. 4, 501-518 (1999). MSC: 60G50 60F05 60J65 82C41 PDF BibTeX XML Cite \textit{B. Davis}, Probab. Theory Relat. Fields 113, No. 4, 501--518 (1999; Zbl 0930.60041) Full Text: DOI OpenURL
Horváth, Lajos; Shao, Qi-Man Limit distributions of directionally reinforced random walks. (English) Zbl 0911.60008 Adv. Math. 134, No. 2, 367-383 (1998). Reviewer: L.G.Gorostiza (Mexico City) MSC: 60F05 60G50 60K40 PDF BibTeX XML Cite \textit{L. Horváth} and \textit{Q.-M. Shao}, Adv. Math. 134, No. 2, 367--383 (1998; Zbl 0911.60008) Full Text: DOI OpenURL
Davis, Burgess Perturbed random walks and Brownian motions, and local times. (English) Zbl 0903.60054 New York J. Math. 3A, 81-87 (1998). Reviewer: A.Khorunzhy (Khar’kov) MSC: 60G50 60F05 60J65 82C41 PDF BibTeX XML Cite \textit{B. Davis}, New York J. Math. 3A, 81--87 (1998; Zbl 0903.60054) Full Text: EuDML EMIS OpenURL
Tóth, B. Limit theorems for weakly reinforced random walks on \(\mathbb{Z}\). (English) Zbl 0912.60043 Stud. Sci. Math. Hung. 33, No. 1-3, 321-337 (1997). Reviewer: Petr Lachout (Praha) MSC: 60F05 60J55 82C41 60G50 PDF BibTeX XML Cite \textit{B. Tóth}, Stud. Sci. Math. Hung. 33, No. 1--3, 321--337 (1997; Zbl 0912.60043) OpenURL
Othmer, Hans G.; Stevens, Angela Aggregation, blowup, and collapse: the ABC’s of taxis in reinforced random walks. (English) Zbl 0990.35128 SIAM J. Appl. Math. 57, No. 4, 1044-1081 (1997). MSC: 35Q80 60J99 92B05 PDF BibTeX XML Cite \textit{H. G. Othmer} and \textit{A. Stevens}, SIAM J. Appl. Math. 57, No. 4, 1044--1081 (1997; Zbl 0990.35128) Full Text: DOI OpenURL
Davis, B. Reinforced random walk. (English) Zbl 0665.60077 Probab. Theory Relat. Fields 84, No. 2, 203-229 (1990). Reviewer: B.Davis MSC: 60J65 60J45 30C85 PDF BibTeX XML Cite \textit{B. Davis}, Probab. Theory Relat. Fields 84, No. 2, 203--229 (1990; Zbl 0665.60077) Full Text: DOI OpenURL