Geodesic
Toeplitz quotient $C^*$-algebras and ratio limits for random walks
Documenta mathematica, Tome 26 (2021), pp. 1529-1556.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 60G50, 60J50, 47L80, 60J10, 37A55, 46L40
Keywords: random walks, strong ratio limit property, ratio limit boundary, Martin boundary, Cuntz algebras, Toeplitz quotients, gauge-invariant uniqueness, symmetry equivariance, subproduct systems 
@article{DOCMA_2021__26__a16,
     author = {Dor-On, Adam},
     title = {Toeplitz quotient {\(C^*\)-algebras} and ratio limits for random walks},
     journal = {Documenta mathematica},
     pages = {1529--1556},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a16/}
}
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Dor-On, Adam. Toeplitz quotient \(C^*\)-algebras and ratio limits for random walks. Documenta mathematica, Tome 26 (2021), pp. 1529-1556. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a16/