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Localization transition of d-friendly walkers
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  • Published: April 2003

Localization transition of d-friendly walkers

  • Hideki Tanemura1 &
  • Nobuo Yoshida2 

Probability Theory and Related Fields volume 125, pages 593–608 (2003)Cite this article

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  • 3 Citations

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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 .

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Authors and Affiliations

  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

    Hideki Tanemura

  2. Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. e-mail: nobuo@kusm.kyoto-u.ac.jp, , , , , , JP

    Nobuo Yoshida

Authors
  1. Hideki Tanemura
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  2. Nobuo Yoshida
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Additional information

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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  • Issue Date: April 2003

  • DOI: https://doi.org/10.1007/s00440-002-0253-z

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Keywords

  • Localization Transition
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