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Published June 2014 | Version Submitted
Journal Article Open

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

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Weizmann Institute of Science

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.

Additional Information

© 2014 Académie des sciences. Published by Elsevier Masson SAS. Received 4 February 2014, Accepted 7 March 2014, Available online 13 May 2014. Presented by Jean-François Le Gall. We thank Ronen Eldan and Cyrille Lucas for many enlightening discussions. During the research, J.C. was a student at the Weizmann Institute of Science, supported by the Israel Science Foundation. G.K. is the incumbent of the Erica and Ludwig Jesselson chair, and was partially supported by the Israel Science Foundation.

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Additional details

Identifiers

Eprint ID
47298
Resolver ID
CaltechAUTHORS:20140717-121031396

Related works

Describes
http://arxiv.org/abs/1401.1036 (URL)

Funding

Israel Science Foundation

Dates

Created
2014-07-17
Created from EPrint's datestamp field
Updated
2021-11-10
Created from EPrint's last_modified field