 028 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 onedimensional simple random walks
$\{ \tl{S}^k_n \}_{n\ge 0}$, $k=1,2,\dots, d+1$ by
introducing ``noncrossing 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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