Abstract:
Consider two configurations, C_1 and C_2, in Bernoulli bond percolation on a general graph G. Take the set S of edges where one endpoint belongs to the cluster of a given vertex “a” in C_1. Now, construct a new configuration that matches C_1 on S and C_2 outside of S; this configuration will retain the same Bernoulli distribution. We identify a broader class of sets S with this property and leverage them to derive new bounds on the three-point function. We discuss the applications of these inequalities to the recent disprove of the bunkbed conjecture.
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