Power-law decay of weights and recurrence of the two-dimensional VRJP

被引：3

作者：

Kozma, Gady ^{[1
]}

Peled, Ron ^{[2
]}

机构：

[1] Weizmann Inst Sci, Dept Math & Comp Sci, IL-76100 Rehovot, Israel

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2021年 / 26卷

基金：

以色列科学基金会; 欧洲研究理事会;

关键词：

Vertex-reinforced jump process; random walk in random environment; decay of correlations; supersymmetry; LOCALIZATION; MODEL;

D O I：

10.1214/21-EJP639

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：19

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