@article{e4e7106d33314f1c80e218c608e29497,

title = "Power-law decay of weights and recurrence of the two-dimensional VRJP",

abstract = "The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker is biased towards returning to previously visited vertices with the bias depending linearly on the local time at these vertices. We prove that, for any initial bias, the weights sampled from the magic formula on a two-dimensional graph decay at least at a power-law rate. Via arguments of Sabot and Zeng, the result implies that the VRJP is recurrent in two dimensions for any initial bias.",

keywords = "Decay of correlations, Random walk in random environment, Supersymmetry, Vertex-reinforced jump process",

author = "Gady Kozma and Ron Peled",

note = "Publisher Copyright: {\textcopyright} 2021, Institute of Mathematical Statistics. All rights reserved.",

year = "2021",

doi = "10.1214/21-EJP639",

language = "אנגלית",

volume = "26",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}