Vertex-reinforced random walk on Z with sub-square-root weights is recurrent

Jun Chen; Gady Kozma

doi:10.1016/j.crma.2014.03.019

Vertex-reinforced random walk on Z with sub-square-root weights is recurrent

Jun Chen, Gady Kozma

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that vertex-reinforced random walk on Z with weight of order k^α, for α∈[0, 1/2), is recurrent. This confirms a conjecture of Volkov for α<1/2. The conjecture for α∈[1/2, 1) remains open.

Original language	English
Pages (from-to)	521-524
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	6
DOIs	https://doi.org/10.1016/j.crma.2014.03.019
State	Published - Jun 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2014.03.019

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title = "Vertex-reinforced random walk on Z with sub-square-root weights is recurrent",

abstract = "We prove that vertex-reinforced random walk on Z with weight of order kα, for α∈[0, 1/2), is recurrent. This confirms a conjecture of Volkov for α<1/2. The conjecture for α∈[1/2, 1) remains open.",

author = "Jun Chen and Gady Kozma",

year = "2014",

month = jun,

doi = "10.1016/j.crma.2014.03.019",

language = "الإنجليزيّة",

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T1 - Vertex-reinforced random walk on Z with sub-square-root weights is recurrent

AU - Chen, Jun

AU - Kozma, Gady

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N2 - We prove that vertex-reinforced random walk on Z with weight of order kα, for α∈[0, 1/2), is recurrent. This confirms a conjecture of Volkov for α<1/2. The conjecture for α∈[1/2, 1) remains open.

AB - We prove that vertex-reinforced random walk on Z with weight of order kα, for α∈[0, 1/2), is recurrent. This confirms a conjecture of Volkov for α<1/2. The conjecture for α∈[1/2, 1) remains open.

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U2 - 10.1016/j.crma.2014.03.019

DO - 10.1016/j.crma.2014.03.019

M3 - مقالة

SN - 1631-073X

VL - 352

SP - 521

EP - 524

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 6

ER -

Vertex-reinforced random walk on Z with sub-square-root weights is recurrent

Abstract

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