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Pré-Publication, Document De Travail Année : 2017

COLLISIONS OF SEVERAL WALKERS IN RECURRENT RANDOM ENVIRONMENTS

Résumé

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 ≤ 1 or m = d = 2. In the transient case with r ≥ 1, we prove that the walkers meet infinitely often, almost surely, if and only if m = 2 and r ≥ 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.
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Dates et versions

hal-01500123 , version 1 (02-04-2017)
hal-01500123 , version 2 (09-07-2018)
hal-01500123 , version 3 (20-11-2020)

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  • HAL Id : hal-01500123 , version 1

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Alexis Devulder, Nina Gantert, Françoise Pene. COLLISIONS OF SEVERAL WALKERS IN RECURRENT RANDOM ENVIRONMENTS. 2017. ⟨hal-01500123v1⟩
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