02-8 Hideki Tanemura, Nobuo Yoshida
Localization transition of (d+1)-friendly walkers (118K, dvi) Jan 3, 02
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Abstract. Friendly walkers is a stochastic model obtained from independent one-dimensional simple random walks \$\{ \tl{S}^k_n \}_{n\ge 0}\$, \$k=1,2,\dots, d+1\$ by introducing ``non-crossing condition'': \$\tl{S}^1_j \ge \tl{S}^2_j \ge \ldots \ge \tl{S}^{d+1}_j, j=1,2,\dots, n\$ and ``reward for collisions'' characterized by parameters \$\b_1, \ldots, \b_d \ge 0\$. Here, the reward for collisions is described as follows. If there are exactly \$m\$ collisions at time \$j\$, i.e., \$m=\sharp \{1\le k \le d:\tl{S}^k_j = \tl{S}^{k+1}_j \} \ge 1\$, then the probabilistic weight for the walkers increases by multiplicative factor \$\exp (\b_m )\ge 1\$. We study the localization transition of this model in terms of the positivity of the free energy. In particular, we prove the existence of the critical surface in the \$d\$-dimensional space for the parameters \$(\b_1, \ldots, \b_d)\$.

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