Martin boundaries of diffusions and random walks on hyperbolic spaces
Werner Ballmann, Debanjan Nandi, Panagiotis Polymerakis
TL;DR
This paper explores the behavior of diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries, which describe the asymptotic behavior at infinity.
Contribution
It provides new insights into the structure of Martin boundaries for diffusions and random walks on hyperbolic spaces and groups of isometries.
Findings
Characterization of Martin boundaries for diffusions on hyperbolic spaces
Analysis of random walks on isometry groups of hyperbolic spaces
Connections between geometric properties and boundary behavior
Abstract
We discuss certain kinds of diffusions on hyperbolic spaces, associated random walks on discrete groups of isometries of the latter, and their Martin boundaries.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology