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

Brydges, David C, Dahlqvist, Antoine and Slade, Gordon (2011) The strong interaction limit of continuous-time weakly self-avoiding walk. Workshop on Probabilistic Techniques in Statistical Mechanics Celebrating the 65th Birthday of Erwin Bolthausen, Berlin, Germany, October 14–16, 2010. Published in: Deuschel, Jean-Dominique, Gentz, Barbara, König, Wolfgang, von Renesse, Max, Scheutzow, Michael and Schmock, Uwe, (eds.) Probability in Complex Physical Systems. 11 275-287. Springer Berlin Heidelberg, Berlin. ISSN 2190-5614 ISBN 9783642238109

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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.

Item Type: Conference Proceedings
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Antoine Dahlqvist
Date Deposited: 25 Mar 2019 15:22
Last Modified: 25 Mar 2019 15:22

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