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.
Equilibrium measures on trees / Arcozzi N.; Levi M.. - In: COLLECTANEA MATHEMATICA. - ISSN 2038-4815. - ELETTRONICO. - 74:1(2023), pp. 61-79. [10.1007/s13348-021-00336-3]
Equilibrium measures on trees
Arcozzi N.;Levi M.
2023
Abstract
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.File in questo prodotto:
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