| | |
| | |
Stat |
Members: 3645 Articles: 2'506'133 Articles rated: 2609
26 April 2024 |
|
| | | |
|
Article overview
| |
|
Metastable behavior for bootstrap percolation on regular trees | Marek Biskup
; Roberto H. Schonmann
; | Date: |
25 Apr 2009 | Abstract: | 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. | Source: | arXiv, 0904.3965 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |