Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances

Details Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances

2011-10-04

arxiv.org/abs/1110.0581v2

Mathematics

Probability

Scientific paper

Let X= {X_t, t \ge 0} be a continuous time random walk in an environment of i.i.d. random conductances {\mu_e \in [1, \infty), e \in E_d}, where E_d is the set of nonoriented nearest neighbor bonds on the Euclidean lattice Z^d and d\ge 3. Let R = {x \in Z^d: X_t = x for some t \ge 0} be the range of X. It is proved that, for almost every realization of the environment, dim_H (R) = dim_P (R) = 2 almost surely, where dim_H and dim_P denote respectively the discrete Hausdorff and packing dimension. Furthermore, given any set A \subseteq Z^d, a criterion for A to be hit by X_t for arbitrarily large t>0 is given in terms of dim_H(A). Similar results for Bouchoud's trap model in Z^d (d \ge 3) are also proven.

Affiliated with

Also associated with

No associations

Rating

Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances 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 Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Fractal Dimensions of the Ranges of Random Walks in $\Z^d$ Associate with Random Conductances will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267687