Geodesic
Toeplitz quotient $C^*$-algebras and ratio limits for random walks
Documenta mathematica, Tome 26 (2021), pp. 1529-1556 Cet article a éte moissonné depuis la source EMS Press

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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. Our combined results are leveraged to identify a unique 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.
DOI : 10.4171/dm/848
Classification : 37A55, 46L40, 47L80, 60G50, 60J10, 60J50
Mots-clés : random walks, gauge-invariant uniqueness, Martin boundary, strong ratio limit property, ratio limit boundary, Cuntz algebras, Toeplitz quotients, symmetry equivariance, subproduct systems 
@article{10_4171_dm_848,
     author = {Adam Dor-On},
     title = {Toeplitz quotient $C^*$-algebras and ratio limits for random walks},
     journal = {Documenta mathematica},
     pages = {1529--1556},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/848},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/848/}
}
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%J Documenta mathematica
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Adam Dor-On. Toeplitz quotient $C^*$-algebras and ratio limits for random walks. Documenta mathematica, Tome 26 (2021), pp. 1529-1556. doi: 10.4171/dm/848

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