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.
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Keywords: Tree, hyperbolic plane, horocyclic product, quantum complex, Laplacian, positive harmonic functions
Mot clés : Arbre, plan hyperbolique, produit horocyclique, complexe quantique, Laplacien, fonctions harmoniques positives
@article{AIF_2016__66_4_1691_0,
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},
pages = {1691--1731},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {4},
year = {2016},
doi = {10.5802/aif.3048},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3048/}
}
TY - JOUR AU - Bendikov, Alexander AU - Saloff-Coste, Laurent AU - Salvatori, Maura AU - Woess, Wolfgang TI - Brownian motion on treebolic space: positive harmonic functions JO - Annales de l'Institut Fourier PY - 2016 SP - 1691 EP - 1731 VL - 66 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3048/ DO - 10.5802/aif.3048 LA - en ID - AIF_2016__66_4_1691_0 ER -
%0 Journal Article %A Bendikov, Alexander %A Saloff-Coste, Laurent %A Salvatori, Maura %A Woess, Wolfgang %T Brownian motion on treebolic space: positive harmonic functions %J Annales de l'Institut Fourier %D 2016 %P 1691-1731 %V 66 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3048/ %R 10.5802/aif.3048 %G en %F AIF_2016__66_4_1691_0
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. https://aif.centre-mersenne.org/articles/10.5802/aif.3048/
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