Abstract
A classical construction associates to a transient random walk on a discrete group Γ a compact Γ -space ∂MΓ known as the Martin boundary. The resulting crossed product C∗-algebra C(∂MΓ) ⋊ rΓ comes equipped with a one-parameter group of automorphisms given by the Martin kernels that define the Martin boundary. In this paper we study the KMS states for this flow and obtain a complete description when the Poisson boundary of the random walk is trivial and when Γ is a torsion free non-elementary hyperbolic group. We also construct examples to show that the structure of the KMS states can be more complicated beyond these cases.
Original language | English |
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Journal | Monatshefte fur Mathematik |
Volume | 196 |
Issue | 1 |
Pages (from-to) | 15-37 |
Number of pages | 23 |
ISSN | 0026-9255 |
DOIs | |
Publication status | Published - Sept 2021 |
Keywords
- KMS states
- Martin boundary
- Random walks