Non-amenable Cayley graphs of high girth have Pc < Pu and mean-field exponents

Asaf Nachmias; Yuval Peres

doi:10.1214/ECP.v17-2139

Non-amenable Cayley graphs of high girth have P_c < P_u and mean-field exponents

Asaf Nachmias^*, Yuval Peres

^*Corresponding author for this work

University of British Columbia

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Journal	Electronic Communications in Probability
Volume	17
DOIs	https://doi.org/10.1214/ECP.v17-2139
State	Published - 2012
Externally published	Yes

Keywords

Non-amenable graphs
Percolation
Self avoiding walk

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10.1214/ECP.v17-2139

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abstract = "In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., pc < pu. 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.",

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doi = "10.1214/ECP.v17-2139",

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AU - Peres, Yuval

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AB - In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., pc < pu. 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.

KW - Non-amenable graphs

KW - Percolation

KW - Self avoiding walk

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Non-amenable Cayley graphs of high girth have P_c < P_u and mean-field exponents

Abstract

Keywords

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