Change search
ReferencesLink to record
Permanent link

Direct link
The time of bootstrap percolation with dense initial sets
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 42, no 4, 1337-1373 p.Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
2014. Vol. 42, no 4, 1337-1373 p.
National Category
URN: urn:nbn:se:su:diva-114308DOI: 10.1214/12-AOP818OAI: diva2:791135
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2015-05-08Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Holmgren, Cecilia
By organisation
Department of Mathematics
In the same journal
Annals of Probability

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 17 hits
ReferencesLink to record
Permanent link

Direct link