References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

The time of bootstrap percolation with dense initial setsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 42, no 4, 1337-1373 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2014. Vol. 42, no 4, 1337-1373 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-114308DOI: 10.1214/12-AOP818OAI: oai:DiVA.org:su-114308DiVA: diva2:791135
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2015-05-08Bibliographically approved

Let r∈N . In r -neighbour bootstrap percolation on the vertex set of a graph G , vertices are initially infected independently with some probability p . At each time step, the infected set expands by infecting all uninfected vertices that have at least r infected neighbours. When p is close to 1, we study the distribution of the time at which all vertices become infected. Given t=t(n)=o(logn/loglogn) , we prove a sharp threshold result for the probability that percolation occurs by time t in d -neighbour bootstrap percolation on the d -dimensional discrete torus T d n . Moreover, we show that for certain ranges of p=p(n) , the time at which percolation occurs is concentrated either on a single value or on two consecutive values. We also prove corresponding results for the modified d -neighbour rule

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});