Random walk attracted by percolation clusters

Details Random walk attracted by percolation clusters Random walk attracted by percolation clusters

2005-07-04

arxiv.org/abs/math/0507054v1

Electronic Communications in Probability, v. 10, n. 27, p. 263-272, 2005

Mathematics

Probability

13 pages

Scientific paper

Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For $f(t)=e^{\beta t}$ we prove that there is a phase transition in $\beta$, i.e., the random walk is subdiffusive for large $\beta$ and is diffusive for small $\beta$.

Affiliated with

Also associated with

No associations

Rating

Random walk attracted by percolation clusters 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 walk attracted by percolation clusters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random walk attracted by percolation clusters will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-467597