Distribution of sizes of erased loops for loop-erased random walks

Details Distribution of sizes of erased loops for loop-erased random walks Distribution of sizes of erased loops for loop-erased random walks

1997-04-03

arxiv.org/abs/cond-mat/9704026v1

PRE, vol.55, 2093, 1997

Physics

Condensed Matter

Statistical Mechanics

4 pages, RevTex, 3 figures

Scientific paper

10.1103/PhysRevE.55.R2093

We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the probability $P_{st}(l)$ of forming a loop of perimeter $l$ when a bond is added to a random spanning tree on the same graph by the simple relation $P(l)=P_{st}(l)/l$. On $d$-dimensional hypercubical lattices, $P(l)$ varies as $l^{-\sigma}$ for large $l$, where $\sigma=1+2/z$ for $1

Affiliated with

Also associated with

No associations

Rating

Distribution of sizes of erased loops for loop-erased random walks 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 Distribution of sizes of erased loops for loop-erased random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distribution of sizes of erased loops for loop-erased random walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422957