Random walk questions for linear quantum groups

We study the discrete quantum groups $Γ$ whose group algebra has an inner faithful representation of type $π:C^*(Γ)\to M_K(\mathbb C)$. Such a representation can be thought of as coming from an embedding $Γ\subset U_K$. Our main result, concerning a certain class of examples of such quantum groups, is an asymptotic convergence theorem for the random walk on $Γ$. The proof uses various algebraic and probabilistic techniques.

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