Toeplitz quotient C*-algebras and ratio limits for random walks

2021/04/23 by Adam Dor-On, Dor-On, Adam
Mathematics · Medicine · #37A55 #46L40 #47L80. Secondary: 60J10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Neurological and metabolic disorders #Operator Algebras (math.OA) #Primary: 60J50 #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2104.11565

openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Our combined results are leveraged to identify a unique smallest symmetry-equivariant quotient C*-algebra for any symmetric random walk on a hyperbolic group, shedding light on a question of Viselter on C*-algebras of subproduct systems.

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