Self-avoiding walk on nonunimodular transitive graphs
ANNALS OF PROBABILITY(2019)
摘要
We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the bubble diagram converges at criticality, and that the critical two-point function decays exponentially in the distance from the origin. This implies that the critical exponent governing the susceptibility takes its mean-field value, and hence that the number of self-avoiding walks of length n is comparable to the nth power of the connective constant. We also prove that the same results hold for a large class of repulsive walk models with a self-intersection based interaction, including the weakly self-avoiding walk. All of these results apply in particular to the product T-k x Z(d) of a k-regular tree (k >= 3) with Z(d), for which these results were previously only known for large k.
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关键词
Self-avoiding walk,nonunimodular,transitive graph,mean-field,nonamenable,bubble diagram
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