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Quenched and annealed heat kernels on the uniform spanning tree

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The uniform spanning tree (UST) on $Zd$ was constructed by Pemantle in 1991 as the limit of the UST on finite boxes $[-n,n]2$. In this talk I will discuss the form of the heat kernel (i.e. random walk transition probability) on this random graph. I will compare the bounds for the UST with those obtained earlier for supercritical percolation.

This is joint work with Takashi Kumagai and David Croydon.

This talk is part of the Probability series.

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