Equilibrium measures on trees

• Arcozzi, Nicola ^[1] ; Levi, Matteo ^[2]
  1. [1] University of Bologna

     University of Bologna

     Bolonia, Italia

     
  2. [2] Polytechnic University of Turin

     Polytechnic University of Turin

     Torino, Italia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 61-79
• Idioma: inglés
• DOI: 10.1007/s13348-021-00336-3
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• Resumen

  • 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.