Geodesic
Meeting time of independent random walks in random environment
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 257-292

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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.

DOI : 10.1051/ps/2011159
Classification : 60K37
Keywords: random walk in random environment, Sinai's regime, t-stable point, meeting time, coalescing time 
@article{PS_2013__17__257_0,
     author = {Gallesco, Christophe},
     title = {Meeting time of independent random walks in random environment},
     journal = {ESAIM: Probability and Statistics},
     pages = {257--292},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011159},
     mrnumber = {3021319},
     zbl = {1292.60098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011159/}
}
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Gallesco, Christophe. Meeting time of independent random walks in random environment. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 257-292. doi: 10.1051/ps/2011159

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