Abstract.
Friendly walkers is a stochastic model obtained from independent one-dimensional simple random walks {S k j } j≥0 , k=1,2,…,d by introducing ``non-crossing condition'': and ``reward for collisions'' characterized by parameters . 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 (β m )≥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 .
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Received: 13 June 2002 / Revised version: 24 August 2002 Published online: 28 March 2003
Mathematics Subject Classification (2000): 82B41, 82B26, 82D60, 60G50
Key words or phrases: Random walks – Random surfaces – Lattice animals – Phase transitions – Polymers – Random walks
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Tanemura, H., Yoshida, N. Localization transition of d-friendly walkers. Probab. Theory Relat. Fields 125, 593–608 (2003). https://doi.org/10.1007/s00440-002-0253-z
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DOI: https://doi.org/10.1007/s00440-002-0253-z