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The strong interaction limit of continuous-time weakly self-avoiding walk

conference contribution
posted on 2023-06-09, 17:13 authored by David C Brydges, Antoine DahlqvistAntoine Dahlqvist, Gordon Slade
The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb–Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme leads to the strictly self-avoiding walk, in another to simple random walk. These two extremes are interpolated by a new model of a self-repelling walk that we call the “quick step” model. We study the limit both for walks taking a fixed number of steps and for the two-point function.

History

Publication status

  • Published

File Version

  • Submitted version

Journal

Probability in Complex Physical Systems

ISSN

2190-5614

Publisher

Springer Berlin Heidelberg

Volume

11

Page range

275-287

Event name

Workshop on Probabilistic Techniques in Statistical Mechanics Celebrating the 65th Birthday of Erwin Bolthausen

Event location

Berlin, Germany

Event type

workshop

Event date

October 14–16, 2010

Place of publication

Berlin

ISBN

9783642238109

Series

Springer Proceedings in Mathematics

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • No

Peer reviewed?

  • Yes

Editors

Jean-Dominique Deuschel, Max von Renesse, Barbara Gentz, Michael Scheutzow, Wolfgang König, Uwe Schmock

Legacy Posted Date

2019-03-25

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