Sharp thresholds in Bootstrap percolation

被引：20

作者：

Balogh, J

Bollobás, B

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[2] Ohio State Univ, Columbus, OH 43210 USA

[3] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2003年 / 326卷 / 3-4期

关键词：

percolation; bootstrap percolation; cellular automata; threshold; sharp threshold;

D O I：

10.1016/S0378-4371(03)00364-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In the standard bootstrap percolation on the d-dimensional grid G(n)(d), in the initial position each of the n(d) sites is occupied with probability p and empty with probability 1 - p, independently of the state of every other site. Once a site is occupied, it remains occupied for ever, while an empty site becomes occupied if at least two of its neighbours are occupied. If at the end of the process every site is occupied, we say that the (initial) configuration percolates. By making use of a theorem of Friedgut and Kalai (Proc. Amer. Math. Soc. 124 (1996) 2993), we shall show that the threshold function of the percolation is sharp. We shall prove-similar results for three other models of bootstrap percolation as well. (C) 2003 Published by Elsevier B.V.

引用

页码：305 / 312

页数：8