Brownian motion on treebolic space: positive harmonic functions
Annales de l'Institut Fourier, Volume 66 (2016) no. 4, p. 1691-1731

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.

Ce travail est dedié à une étude de la théorie du potentiel sur l’espace arbolique, i.e., le produit horcyclique d’un ârbre régulier avec le demi-plan hyperbolique supérieur. En se basant sur l’analyse sur les complexes à bandes Riemanniennes développée par les auteurs, on considère une famille de Laplaciens avec deux paramètres concernant la dérive verticale. On examine les fonctions harmoniques associées à ces Laplaciens.

Received : 2015-03-24
Revised : 2015-11-15
Accepted : 2015-12-21
Published online : 2016-07-28
Classification:  31C05,  60J50,  53C23,  05C05
Keywords: Tree, hyperbolic plane, horocyclic product, quantum complex, Laplacian, positive harmonic functions
     author = {Bendikov, Alexander and Saloff-Coste, Laurent and Salvatori, Maura and Woess, Wolfgang},
     title = {Brownian motion on treebolic space: positive harmonic functions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {4},
     year = {2016},
     pages = {1691-1731},
     doi = {10.5802/aif.3048},
     language = {en},
     url = {}
Bendikov, Alexander; Saloff-Coste, Laurent; Salvatori, Maura; Woess, Wolfgang. Brownian motion on treebolic space: positive harmonic functions. Annales de l'Institut Fourier, Volume 66 (2016) no. 4, pp. 1691-1731. doi : 10.5802/aif.3048.

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