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Random walks on groups and KMS states

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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.

TidsskriftMonatshefte fur Mathematik
Sider (fra-til)15-37
Antal sider23
StatusUdgivet - sep. 2021

Bibliografisk note

Funding Information:
The work was supported by the DFF-Research Project 2 ‘Automorphisms and Invariants of Operator Algebras’, No. 7014-00145B.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

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