Random walks in random Dirichlet environment are transient in dimension $d\ge 3$

Details Random walks in random Dirichlet environment are transient in dimension $d\ge 3$ Random walks in random Dirichlet environment are transient in dimension $d\ge 3$

2008-11-26

arxiv.org/abs/0811.4285v3

Mathematics

Probability

New version published at PTRF with an analytic proof of lemma 1

Scientific paper

We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are parameterized by a $2d$-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension $d\ge 3$. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and applies for example to finitely generated symmetric transient Cayley graphs. In terms of reinforced random walks it implies that directed edge reinforced random walks are transient for $d\ge 3$.

Affiliated with

Also associated with

No associations

Rating

Random walks in random Dirichlet environment are transient in dimension $d\ge 3$ 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 Random walks in random Dirichlet environment are transient in dimension $d\ge 3$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random walks in random Dirichlet environment are transient in dimension $d\ge 3$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274430