Uniqueness and non-uniqueness in percolation theory
نویسندگان
چکیده
منابع مشابه
Uniqueness and non-uniqueness in percolation theory
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on Z d and, more generally, on transitive graphs. For iid percolation on Z, uniqueness of the infinite cluster is a classical result, while on certain other transitive graphs uniqueness may fail. Key properties of the graphs in this context turn out to be amenability ...
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Two results on site percolation on the d-dimensional lattice, d^l arbitrary, are presented. In the first theorem, we show that for stationary underlying probability measures, each infinite cluster has a well-defined density with probability one. The second theorem states that if in addition, the probability measure satisfies the finite energy condition of Newman and Schulman, then there can be ...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2006
ISSN: 1549-5787
DOI: 10.1214/154957806000000096