The Whishart–Pickrell Distributions and Closures of Group Actions


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Consider probability distributions on the space of infinite Hermitian matrices Herm(∞) invariant with respect to the unitary group U(∞). We describe the closure of U(∞) in the semigroup of spreading maps (polymorphisms) of Herm(∞); this closure is a semigroup isomorphic to the semigroup of all contractive operators.

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Yu. Neretin

University of Vienna, Vienna, Austria; Institute for Theoretical and Experimental Physics; Moscow State University; Institute for Information Transmission Problems

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Email: neretin@mccme.ru
俄罗斯联邦, Moscow

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