Random walks on Baumslag-Solitar groups

Cuno, Johannes; Sava-Huss, Ecaterina

doi:10.48550/arxiv.1510.00833

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2016

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“…Also of interest: to replace the tree by the 1-skeleton of a higher-dimensional A d -building, or just to take different types of level functions on a regular tree; compare e.g. with the space considered by Cuno and Sava-Huss [12].…”

Section: Figurementioning

confidence: 99%

Brownian motion on treebolic space: positive harmonic functions

Bendikov¹,

Saloff‐Coste²,

Salvatori³

et al. 2016

Annales De l'Institut Fourier

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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. Mouvement Brownien sur l'espace arbolique: fonctions harmoniques positivesRésumé. Ce travail est dedié a une etude de la théorie du potentiel sur l'espace arbolique, i.e., le produit horcyclique d'unârbre régulier avec le demi plan hyperbolique superieur. En se basant sur l'analyse sur les complexes a bandes Riemanniennes developée par les auteurs, on considère une famille de Laplaciens avec deux paramètres concernant la dérive verticale. On examine les fonctions harmoniques associées a ces Laplaciens.

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Section: Figurementioning

confidence: 99%