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Non-amenable Cayley graphs of high girth have $p_c < p_u$ and mean-field exponents


 
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1. Title Title of document Non-amenable Cayley graphs of high girth have $p_c < p_u$ and mean-field exponents
 
2. Creator Author's name, affiliation, country Asaf Nachmias; University of British Columbia; Canada
 
2. Creator Author's name, affiliation, country Yuval Peres; Microsoft Research; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Percolation; Self avoiding walk; Non-amenable graphs
 
3. Subject Subject classification 82B43
 
4. Description Abstract In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., $p_c< p_u$. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-12-03
 
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/2139
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-2139
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
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