Random walks on groups and KMS states

Johannes Christensen, Klaus Thomsen*

*Corresponding author af dette arbejde

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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


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