Volume 17, 2013
|Page(s)||257 - 292|
|Published online||08 February 2013|
Meeting time of independent random walks in random environment
Instituto de Matemática e Estatística, Universidade de São
Paulo, rua do Matão 1010, CEP
Received: 11 September 2010
Revised: 10 August 2011
We consider, in the continuous time version, γ independent random walks on Z+ in random environment in Sinai’s regime. Let Tγ be the first meeting time of one pair of the γ random walks starting at different positions. We first show that the tail of the quenched distribution of Tγ, after a suitable rescaling, converges in probability, to some functional of the Brownian motion. Then we compute the law of this functional. Eventually, we obtain results about the moments of this meeting time. Being Eω the quenched expectation, we show that, for almost all environments ω, Eω[Tγc] is finite for c < γ(γ − 1) / 2 and infinite for c > γ(γ − 1) / 2.
Mathematics Subject Classification: 60K37
Key words: Random walk in random environment / Sinai’s regime / t-stable point / meeting time / coalescing time
© EDP Sciences, SMAI, 2013
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