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Percolation Beyond $Z^d$, Many Questions And a Few Answers


 
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1. Title Title of document Percolation Beyond $Z^d$, Many Questions And a Few Answers
 
2. Creator Author's name, affiliation, country Itai Benjamini; Weizmann Institute of Science
 
2. Creator Author's name, affiliation, country Oded Schramm; Microsoft Research
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Percolation, criticality, planar graph, transitive graph, isoperimetericinequality
 
3. Subject Subject classification 82B43, 60K35
 
4. Description Abstract A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $p_c$ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $p>p_c$ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.
 
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7. Date (YYYY-MM-DD) 1996-10-08
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/978
 
10. Identifier Digital Object Identifier 10.1214/ECP.v1-978
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 1
 
12. Language English=en
 
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