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.
Mots-clés : 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://archive.numdam.org/articles/10.1051/ps/2011159/}
}
TY - JOUR AU - Gallesco, Christophe TI - Meeting time of independent random walks in random environment JO - ESAIM: Probability and Statistics PY - 2013 SP - 257 EP - 292 VL - 17 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2011159/ DO - 10.1051/ps/2011159 LA - en ID - PS_2013__17__257_0 ER -
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. http://archive.numdam.org/articles/10.1051/ps/2011159/
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