Metastable behavior for bootstrap percolation on regular trees

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

10 pages, version to appear in J. Statist. Phys

Scientific paper

10.1007/s10955-009-9798-x

We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least theta occupied neighbors, occupied sites remain occupied forever. It is known that, when b>theta>1, the limiting density q=q(p) of occupied sites exhibits a jump at some p_t=p_t(b,theta) in (0,1) from q_t:=q(p_t)<1 to q(p)=1 when p>p_t. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p_t+h with h>0 and show that, as h decreases to 0, the system lingers around the "critical" state for time order h^{-1/2} and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q in (q_t,1) converges, as h tends to 0, to a well-defined measure.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Metastable behavior for bootstrap percolation on regular trees 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 Metastable behavior for bootstrap percolation on regular trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metastable behavior for bootstrap percolation on regular trees will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-671290

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.