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Collisions of several walkers in recurrent random environments. (arXiv:1807.04019v1 [math.PR])
来源于:arXiv
We consider d independent walkers on Z, m of them performing simple symmetric
random walk and r = d -- m of them performing recurrent RWRE (Sinai walk), in I
independent random environments. We show that the product is recurrent, almost
surely, if and only if m $\le$ 1 or m = d = 2. In the transient case with r
$\ge$ 1, we prove that the walkers meet infinitely often, almost surely, if and
only if m = 2 and r $\ge$ I = 1. In particular, while I does not have an
influence for the recurrence or transience, it does play a role for the
probability to have infinitely many meetings. To obtain these statements, we
prove two subtle localization results for a single walker in a recurrent random
environment, which are of independent interest. 查看全文>>