Equilibrium measures on trees
arXiv:1811.05194 · doi:10.1007/s13348-021-00336-3
Abstract
We give a characterization of equilibrium measures for -capacities on the boundary of an infinite tree of arbitrary (finite) local degree. For , 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.
Major changes in the exposition, no changes in the results. Technical section on regularity of boundaries, of independent interest, removed to lighten the contents. 17 pages, 2 figure