Metastable Behavior for Bootstrap Percolation on Regular Trees

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F09%3A00011107" target="_blank" >RIV/60076658:12510/09:00011107 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Metastable Behavior for Bootstrap Percolation on Regular Trees

Popis výsledku v původním jazyce

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 ? occupied neighbors, occupied sites remain occupied forever. It is known that, when b > 8 >= 2, the limiting density q = q(p) of occupied sites exhibits a jump at some pT = pT(b, 8) (0, 1) from qT := q(pT) < 1 to q(p) = 1 when p > pT. We investigate the metastable behavior associated with this transition. Explicitly, we pick p = pT + h with h>0 and show that, as h 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 occupationdensity is q (qT, 1) converges, as h 0, to a well-defined measure.

Název v anglickém jazyce

Metastable Behavior for Bootstrap Percolation on Regular Trees

Popis výsledku anglicky

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 ? occupied neighbors, occupied sites remain occupied forever. It is known that, when b > 8 >= 2, the limiting density q = q(p) of occupied sites exhibits a jump at some pT = pT(b, 8) (0, 1) from qT := q(pT) < 1 to q(p) = 1 when p > pT. We investigate the metastable behavior associated with this transition. Explicitly, we pick p = pT + h with h>0 and show that, as h 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 occupationdensity is q (qT, 1) converges, as h 0, to a well-defined measure.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

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Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Statistical Physics

ISSN

0022-4715

e-ISSN

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Svazek periodika

136

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

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Kód UT WoS článku

000269885000004

EID výsledku v databázi Scopus

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