Geodesic
Wishart–Pickrell distributions and closures of group actions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 236-245
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Consider probability distributions on the space of infinite Hermitian matrices $\mathrm{Herm}(\infty)$ invariant with respect to the unitary group $\mathrm U(\infty)$. We describe the closure of $\mathrm U(\infty)$ in the space of spreading maps (polymorphisms) of $\mathrm{Herm}(\infty)$; this closure is a semigroup isomorphic to the semigroup of all contractive operators. 
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     title = {Wishart{\textendash}Pickrell distributions and closures of group actions},
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Yu. A. Neretin. Wishart–Pickrell distributions and closures of group actions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 236-245. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a14/

[1] E. Glasner, B. Tsirelson, B. Weiss, “The automorphism group of the Gaussian measure cannot act pointwise”, Israel J. Math., 148 (2005), 305–329 | DOI | MR | Zbl

[2] R. E. Howe, C. C. Moore, “Asymptotic properties of unitary representations”, J. Funct. Anal., 32:1 (1979), 72–96 | DOI | MR | Zbl

[3] U. Krengel, Ergodic Theorems, Walter de Gruyter Co., Berlin, 1985 | MR | Zbl

[4] E. Nelson, “The free Markoff field”, J. Funct. Anal., 12 (1973), 211–227 | DOI | MR | Zbl

[5] Yu. A. Neretin, Kategorii simmetrii i beskonechnomernye gruppy, URSS, M., 1998

[6] Yu. A. Neretin, “Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation”, Zap. nauchn. semin. POMI, 292, 2002, 62–91 | MR | Zbl

[7] Yu. A. Neretin, “Symmetries of Gaussian measures and operator colligations”, J. Funct. Anal., 263:3 (2012), 782–802 | DOI | MR | Zbl

[8] G. I. Olshanskii, “Unitarnye predstavleniya beskonechnomernykh klassicheskikh grupp $\mathrm U(p,\infty)$, $\mathrm{SO}_0(p,\infty)$, $\mathrm{Sp}(p,\infty)$ i sootvetstvuyuschikh grupp dvizhenii”, Funkts. analiz i ego pril., 12:3 (1978), 32–44 | MR | Zbl

[9] G. Olshanski, A. Vershik, “Ergodic unitarily invariant measures on the space of infinite Hermitian matrices”, Contemporary Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 175, Amer. Math. Soc., Providence, RI, 1996, 137–175 | DOI | MR | Zbl

[10] A. M. Vershik, “Mnogoznachnye otobrazheniya s invariantnoi meroi (polimorfizmy) i markovskie operatory”, Zap. nauchn. semin. LOMI, 72, 1977, 26–61 | MR | Zbl

[11] D. Pickrell, “Mackey analysis of infinite classical motion groups”, Pacific J. Math., 150:1 (1991), 139–166 | DOI | MR | Zbl