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Locality of critical points: the connective constant

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Is the numerical value of a critical point a continuous function of the underlying graph? I shall discuss this question in general, and then concentrate on the problem of counting self-avoiding walks (SAWs). It turns out that this problem is related to bridge-decompositions of SAWs, and, in the case of Cayley graphs, to the existence of linearly growing harmonic functions that respect the group structure. [Joint work with Zhongyang Li.]

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