3 years ago

Equilibrium measures on trees.

Nicola Arcozzi, Matteo Levi

We give a characterization of equilibrium measures for $p$-capacities on the boundary of an infinite tree of locally bounded degree. For $p=2$, this provides, in the special case of trees, a converse to a theorem of Benjamini and Schramm, which interpretes the equilibrium measure of a planar graph's boundary in terms of square tilings of cylinders.

Publisher URL: http://arxiv.org/abs/1811.05194

DOI: arXiv:1811.05194v1

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