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Mathematics > Probability

arXiv:1812.01816 (math)
[Submitted on 5 Dec 2018 (v1), last revised 14 Jul 2023 (this version, v6)]

Title:Besov spaces and random walks on a hyperbolic group: boundary traces and reflecting extensions of Dirichlet forms

Authors:Pierre Mathieu, Yuki Tokushige
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Abstract:We show the existence of a trace process at infinity for random walks on hyperbolic groups of conformal dimension < 2 and relate it to the existence of a reflecting random walk. To do so, we employ the theory of Dirichlet forms which connects the theory of symmetric Markov processes to functional analytic perspectives. We introduce a family of Besov spaces associated to random walks and prove that they are isomorphic to some of the Besov spaces constructed from the co-homology of the group studied in Bourdon-Pajot (2003). We also study the regularity of harmonic measures of random walks on hyperbolic groups using the potential theory associated to Dirichlet forms.
Comments: 47 pages, the title has been changed
Subjects: Probability (math.PR)
Cite as: arXiv:1812.01816 [math.PR]
  (or arXiv:1812.01816v6 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.01816

Submission history

From: Yuki Tokushige [view email]
[v1] Wed, 5 Dec 2018 04:57:05 UTC (30 KB)
[v2] Tue, 12 Feb 2019 11:07:54 UTC (31 KB)
[v3] Sun, 5 May 2019 10:06:59 UTC (32 KB)
[v4] Sat, 1 Jun 2019 06:12:31 UTC (33 KB)
[v5] Sat, 4 Jun 2022 02:58:08 UTC (47 KB)
[v6] Fri, 14 Jul 2023 15:16:16 UTC (50 KB)
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