Toeplitz Quotient C*-Algebras and Ratio Limits for Random Walks

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We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent ratios of transition probabilities. These C*-algebras give rise to new notions of ratio limit space and boundary for such random walks, which are computed by appealing to a companion paper by Woess.

Original languageEnglish
Pages (from-to)1529-1556
Number of pages28
JournalDocumenta Mathematica
StatePublished - 2021
Externally publishedYes


  • Cuntz algebras
  • Gauge-invariant uniqueness
  • Martin boundary
  • Random walks
  • Ratio limit boundary
  • Strong ratio limit property
  • Subproduct systems
  • Symmetry equivariance
  • Toeplitz quotients

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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