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Alexander Bendikov; Laurent Saloff-Coste; Maura Salvatori; Wolfgang Woess
Brownian motion on treebolic space: positive harmonic functions
(Mouvement Brownien sur l’espace arbolique : fonctions harmoniques positives)
Annales de l'institut Fourier, 66 no. 4 (2016), p. 1691-1731, doi: 10.5802/aif.3048
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Class. Math.: 31C05, 60J50, 53C23, 05C05
Keywords: Tree, hyperbolic plane, horocyclic product, quantum complex, Laplacian, positive harmonic functions

Résumé - Abstract

This paper studies potential theory on treebolic space, that is, the horocyclic product of a regular tree and hyperbolic upper half plane. Relying on the analysis on strip complexes developed by the authors, a family of Laplacians with “vertical drift” parameters is considered. We investigate the positive harmonic functions associated with those Laplacians.

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