Equilibrium measures on trees
| Autor: | Nicola Arcozzi, Matteo Levi |
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| Rok vydání: | 2021 |
| Předmět: |
Degree (graph theory)
Applied Mathematics General Mathematics Boundary (topology) Tree (graph theory) Measure (mathematics) Square (algebra) Planar graph Combinatorics symbols.namesake Mathematics - Classical Analysis and ODEs Primary: 31C15. Secondary: 05C63 05C05 05B45 52C20 Converse Classical Analysis and ODEs (math.CA) FOS: Mathematics symbols Mathematics - Combinatorics Combinatorics (math.CO) Special case Mathematics |
| Zdroj: | Collectanea Mathematica. 74:61-79 |
| ISSN: | 2038-4815 0010-0757 |
| Popis: | 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. 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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