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On invariant random positive definite functions

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arxiv 1804.10471 v1 pith:5RTKCYJE submitted 2018-04-27 math.GR math.OAmath.RT

Vadim Alekseev , Rahel Brugger This is my paper · ORCID
classification math.GRmath.OAmath.RT
keywords invariantrandomdefinitepositivecharacterfunctionsalgebrasclasses
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We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random positive definite functions on groups with infinite conjugacy classes which integrate to the regular character are constant.

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  1. Stationary characters on lattices of semisimple Lie groups

    math.GR 2019-08 accept novelty 8.0 of 10

    Every stationary character on an irreducible lattice of a higher-rank semisimple Lie group is a genuine character, yielding new rigidity and URS finiteness results.

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