Toeplitz quotient -algebras and ratio limits for random walks
Adam Dor-On
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
![Toeplitz quotient $C^*$-algebras and ratio limits for random walks cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-26.png&w=3840&q=90)
Abstract
We study quotients of the Toeplitz -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 -algebra for random walks that have convergent ratios of transition probabilities. These -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 symmetry-equivariant quotient -algebra for any symmetric random walk on a hyperbolic group, shedding light on a question of Viselter on -algebras of subproduct systems.
Cite this article
Adam Dor-On, Toeplitz quotient -algebras and ratio limits for random walks. Doc. Math. 26 (2021), pp. 1529–1556
DOI 10.4171/DM/848