Geodesic
A generalized Maxwell--Poincar\'e lemma and Wishart measures
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 15-25

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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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     author = {A. M. Vershik and F. V. Petrov},
     title = {A generalized {Maxwell--Poincar\'e} lemma and {Wishart} measures},
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     volume = {507},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a1/}
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A. M. Vershik; F. V. Petrov. A generalized Maxwell--Poincar\'e 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/