Equilibrium measures on trees
Classical Analysis and ODEs
2023-04-18 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1811.05194,
title = {Equilibrium measures on trees},
author = {Nicola Arcozzi and Matteo Levi},
journal= {arXiv preprint arXiv:1811.05194},
year = {2023}
}
Comments
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