Mathematics – Probability
Scientific paper
2009-03-27
Mathematics
Probability
70 pages, 10 figures
Scientific paper
We consider, in the continuous time version, $\gamma$ independent random walks on $\mathbb{Z_+}$ in random environment in the Sinai's regime. Let $T_\gam$ be the first meeting time of one pair of the $\gamma$ random walks starting at different positions. We first show that the tail of the quenched distribution of $T_\gamma$, 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 $\Eo$ the quenched expectation, we show that, for almost all environments $\omega$, $\Eo[T_\gamma^{c}]$ is finite for $c<\gamma(\gamma-1)/2$ and infinite for $c>\gamma(\gamma-1)/2$.
Gallesco Christophe
No associations
LandOfFree
On the moments of the meeting time of independent random walks in random environment does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the moments of the meeting time of independent random walks in random environment, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the moments of the meeting time of independent random walks in random environment will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-20962