Localization transition of d-friendly walkers

Hideki Tanemura, Nobuo Yoshida

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Friendly walkers is a stochastic model obtained from independent one-dimensional simple random walks {Sjk}j≥0, k = 1, 2,..., d by introducing "non-crossing condition": Sj1 ≤ Sj2 ≤ ... ≤ Sjd, j = 1,2, ..., n and "reward for collisions" characterized by parameters β2, ..., βd ≥ 0. Here, the reward for collisions is described as follows. If, at a given time n, a site in ℤ is occupied by exactly m ≥ 2 walkers, then the site increases the probabilistic weight for the walkers by multiplicative factor exp(βm) ≥ 1. We study the localization transition of this model in terms of the positivity of the free energy and describe the location and the shape of the critical surface in the (d - 1)-dimensional space for the parameters (β2,..., βd).

Original languageEnglish
Pages (from-to)593-608
Number of pages16
JournalProbability Theory and Related Fields
Volume125
Issue number4
DOIs
Publication statusPublished - 2003 Apr 1
Externally publishedYes

Keywords

  • Lattice animals
  • Phase transitions
  • Polymers
  • Random surfaces
  • Random walks

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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