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This article is available for purchase or by subscription. See below.
Abstract
We construct a one-to-one continuous map from the Morse boundary of a
hierarchically hyperbolic group to its Martin boundary. This construction is based
on deviation inequalities generalizing Ancona’s work on hyperbolic groups.
This provides a possibly new metrizable topology on the Morse boundary
of such groups. We also prove that the Morse boundary has measure
0 with
respect to the harmonic measure unless the group is hyperbolic.
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Keywords
random walk, Ancona inequalities, hierarchically hyperbolic
group, relatively hyperbolic group
Mathematical Subject Classification 2010
Primary: 20P05, 20F65, 60J50
Secondary: 20F67, 31C35
Publication
Received: 21 May 2020
Revised: 12 May 2021
Accepted: 1 July 2021
Published: 25 August 2022