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Local Bootstrap Percolation


 
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1. Title Title of document Local Bootstrap Percolation
 
2. Creator Author's name, affiliation, country Janko Gravner; University of California Davis
 
2. Creator Author's name, affiliation, country Alexander E. Holroyd; University of British Columbia, Microsoft Research
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) bootstrap percolation; cellular automaton; crossover; finite-size scaling; metastability
 
3. Subject Subject classification Primary 60K35; Secondary 82B43
 
4. Description Abstract We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of $\mathbb{Z}^2$ are independently occupied with small probability $p$, otherwise empty. Subsequently, an empty site becomes active by contact with two or more active neighbors, and an occupied site becomes active if it has an active site within distance 2. We prove that the entire lattice becomes active with probability $\exp [\alpha(p)/p]$, where $\alpha(p)$ is between $-\pi^2/9+c\sqrt p$ and $-\pi^2/9+C\sqrt p(\log p^{-1})^3$. This corrects previous numerical predictions for the scaling of the correction term.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF (USA); Ministry of Science (Slovenia); NSERC (Canada); Microsoft
 
7. Date (YYYY-MM-DD) 2009-02-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/607
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-607
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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