Resumen de 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 arbitrary (finite) local 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.