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arXiv · 1805.09552

Martin boundaries of the duals of free unitary quantum groups

Sara Malacarne·Sergey Neshveyev
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Abstract

Given a free unitary quantum group $G=A_u(F)$, with $F$ not a unitary $2$-by-$2$ matrix, we show that the Martin boundary of the dual of $G$ with respect to any $G$-$\hat G$-invariant, irreducible, finite range quantum random walk coincides with the topological boundary defined by Vaes and Vander Vennet. This can be thought of as a quantum analogue of the fact that the Martin boundary of a free group coincides with the space of ends of its Cayley tree.

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Sara Malacarne, Sergey Neshveyev. 2018-05-24. Martin boundaries of the duals of free unitary quantum groups. https://doi.org/10.1112/s0010437x19007322

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