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arXiv · 1207.1480

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

Asaf Nachmias·Yuval Peres
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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., 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.

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Asaf Nachmias, Yuval Peres. 2012-12-04. Non-amenable Cayley graphs of high girth have p_c < p_u and mean-field exponents. https://arxiv.org/abs/1207.1480

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