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Random Walks on Finite Quantum Groups

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Abstract

In this paper, we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e., the limit state if it exists. We note that the possible limits are any central idempotent state. We also look at cutoff phenomenon in the Sekine finite quantum groups.

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Acknowledgements

The author would like to thank Haonan Zhang, for providing her with his preprint [17]. This work was supported by the French “Investissements d’Avenir” program, Project ISITE-BFC (Contract ANR-15-IDEX-03).

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  1. Laboratoire de mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, 16 route de Gray, 25030, Besançon Cedex, France

    Isabelle Baraquin

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  1. Isabelle Baraquin
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Correspondence to Isabelle Baraquin.

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Baraquin, I. Random Walks on Finite Quantum Groups. J Theor Probab 33, 1715–1736 (2020). https://doi.org/10.1007/s10959-019-00916-x

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  • DOI: https://doi.org/10.1007/s10959-019-00916-x

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