Geodesic
A generalized Maxwell–Poincaré lemma and Wishart measures
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 15-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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We get a series of degenerate Wishart measures on the space of infinite Hermitian matrices by directly passing to a limit of a sequence of orbital invariant measures on the Stiefel manifold. 
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A. M. Vershik; F. V. Petrov. A generalized Maxwell–Poincaré lemma and Wishart measures. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 15-25. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a1/

[1] 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 | Zbl

[2] A. M. Vershik, “Opisanie invariantnykh mer dlya deistvii nekotorykh beskonechnomernykh grupp”, DAN SSSR, 218:4 (1974), 749–752 | Zbl

[3] A. M. Vershik, Suschestvuet li lebegova mera v beskonechnomernom prostranstve?, Trudy Inst. Mat. im V. A. Steklova, 259, 2007, 256–281 | Zbl

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

[5] T. Assiotis, “Ergodic decomposition for inverse Wishart measures on infinite positive-definite matrices”, SIGMA, 15 (2019), 067 | MR | Zbl

[6] J. Wishart, “The generalized product moment distribution in samples from a normal multivariate population”, Biometrika, 20A (1928), 32–52 | DOI | Zbl

[7] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd edition, Wiley Interscience, Hoboken, NJ, 2003 | Zbl

[8] Yu. Baryshnikov, “GUEs and queues”, Probab. Theory Related Fields, 119 (2001), 256–274 | DOI | MR | Zbl

[9] L. N. Dovbysh, V. N. Sudakov, “O matritsakh Grama–de Finetti”, Zap. nauchn. semin. LOMI, 119, 1982, 77–86 | MR | Zbl

[10] T. Austin, “Exchangeable random measures”, Ann. Inst. H. Poincaré Probab. Statist., 51:3 (2015), 842–861 | Zbl

[11] A. M. Vershik, “Tri teoremy edinstvennosti mery Plansherelya s razlichnykh tochek zreniya”, Trudy Inst. Mat. im V. A. Steklova, 305, 2019, 63–77 | Zbl

[12] G. Olshanski, “Unitary representations of infinite-dimensional pairs $(G,K)$ and the formalism of R. Howe”, Representations of Lie groups and related topics, eds. A. M. Vershik, D. P. Zhelobenko, Gordon and Breach, New York, 1990, 269–463

[13] K. Johansson, E. Nordenstam, “Eigenvalues of GUE minors”, Electron. J. Probab., 11:50 (2006), 1342–1371 | MR | Zbl