Brownian motion on treebolic space: positive harmonic functions
[Mouvement Brownien sur l’espace arbolique : fonctions harmoniques positives]
Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1691-1731.

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.

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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DOI : 10.5802/aif.3048
Classification : 31C05, 60J50, 53C23, 05C05
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
Bendikov, Alexander 1 ; Saloff-Coste, Laurent 2 ; Salvatori, Maura 3 ; Woess, Wolfgang 4

1 Insitute of Mathematics Wroclaw University Pl. Grundwaldzki 2/4 50-384 Wroclaw, Poland
2 Department of Mathematics Cornell University Ithaca, NY 14853, USA
3 Dipartimento di Matematica Università di Milano Via Saldini 50 20133 Milano, Italy
4 Institut für Diskrete Mathematik Technische Universität Graz Steyrergasse 30 A-8010 Graz, Austria
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Bendikov, Alexander; Saloff-Coste, Laurent; Salvatori, Maura; Woess, Wolfgang. Brownian motion on treebolic space: positive harmonic functions. Annales de l'Institut Fourier, Tome 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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