Localization transition of <Emphasis Type="Italic">d</Emphasis>-friendly walkers |
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Authors: | Hideki Tanemura Nobuo Yoshida |
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Institution: | (1) Department of Mathematics and Informatics, Faculty of Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan. e-mail: tanemura@math.s.chiba-u.ac.jp, JP;(2) Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. e-mail: nobuo@kusm.kyoto-u.ac.jp, JP |
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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 .
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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Keywords: | |
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