Stability of infinite clusters in supercritical percolation

被引：0

作者：

Roberto H. Schonmann

机构：

[1] Mathematics Department,

[2] University of California at Los Angeles,undefined

[3] Los Angeles,undefined

[4] CA 90095,undefined

[5] USA (e-mail: rhs@math.ucla.edu),undefined

来源：

Probability Theory and Related Fields | 1999年 / 113卷

关键词：

Mathematics Subject Classification (1991): Primary 60K35; Keywords: Percolation, quasi-transitive graphs, continuity of percolation probability, monotonicity of uniqueness;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

. A recent theorem by Häggström and Peres concerning independent percolation is extended to all the quasi-transitive graphs. This theorem states that if 0<p1<p2≤1 and percolation occurs at level p1, then every infinite cluster at level p2 contains some infinite cluster at level p1. Consequences are the continuity of the percolation probability above the percolation threshold and the monotonicity of the uniqueness of the infinite cluster, i.e., if at level p1 there is a unique infinite cluster then the same holds at level p2. These results are further generalized to graphs with a “uniform percolation” property. The threshold for uniqueness of the infinite cluster is characterized in terms of connectivities between large balls.

引用

页码：287 / 300

页数：13