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 $(\b_1, \ldots, \b_d)$.

Files: 02-8.src( 02-8.keywords , friend7.dvi.mm )