Aarhus University Seal

Random walks on groups and KMS states

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review



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 languageEnglish
JournalMonatshefte fur Mathematik
Pages (from-to)15-37
Number of pages23
Publication statusPublished - Sept 2021

Bibliographical note

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

    Research areas

  • KMS states, Martin boundary, Random walks

See relations at Aarhus University Citationformats

ID: 221416226