Skip to main content
SpringerLink
Log in

A Generalized Maxwell–Poincaré Lemma and Wishart Measures

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We get a series of degenerate Wishart measures on the space of infinite Hermitian matrices by directly passing to the limit of a sequence of orbital invariant measures on the Stiefel manifold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Olshanski and A. Vershik, “Ergodic unitarily invariant measures on the space of infinite Hermitian matrices,” in: Contemporary Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, Vol. 175, Amer. Math. Soc., Providence, Rhode Island (1996), pp. 137–175.

  2. A. M. Vershik, “A description of invariant measures for actions of certain infinitedimensional groups,” Soviet Math. Dokl., 15, No. 5, 139–1400 (1975).

    Google Scholar 

  3. A. M. Vershik, “Does there exist a Lebesgue measure in the infinite-dimensional space?,” Proc. Steklov Inst Math., 259, 248–272 (2007).

    Article  MathSciNet  Google Scholar 

  4. D. Pickrell, “Mackey analysis of infinite classical motion groups,” Pacific J. Math., 150, No. 1, 139–166 (1991).

    Article  MathSciNet  Google Scholar 

  5. T. Assiotis, “Ergodic decomposition for inverse Wishart measures on infinite positivedefinite matrices,” SIGMA, 15, 067 (2019).

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd edition, Wiley Interscience, Hoboken, New Jersey (2003).

    MATH  Google Scholar 

  8. Yu. Baryshnikov, “GUEs and queues,” Probab. Theory Related Fields, 119, 256–274 (2001).

    Article  MathSciNet  Google Scholar 

  9. L. N. Dovbysh and V. N. Sudakov, “Gram–de Finetti matrices,” Zap. Nauchn. Semin. LOMI, 119, 77–86 (1982).

    MathSciNet  MATH  Google Scholar 

  10. T. Austin, “Exchangeable random measure,” Ann. Inst. H. Poincar´e Probab. Statist., 51, No. 3, 842–861 (2015).

    MathSciNet  MATH  Google Scholar 

  11. A. M. Vershik, “Three theorems on the uniqueness of the Plancherel measure from different viewpoints,” Proc. Steklov Inst. Math., 305, No. 1, 63–77 (2019).

    Article  MathSciNet  Google Scholar 

  12. G. Olshanski, “Unitary representations of infinite-dimensional pairs (G,K) and the formalism of R. Howe,” in: A. M. Vershik and D. P. Zhelobenko (eds.), Representations of Lie Groups and Related Topics, Gordon and Breach, New York (1990), pp. 269–463.

  13. K. Johansson and E. Nordenstam, “Eigenvalues of GUE minors,” Electron. J. Probab., 11, No. 50, 1342–1371 (2006).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University, St. Petersburg, Russia

    A. M. Vershik

  2. Institute for Information Transmission Problems, Moscow, Russia

    A. M. Vershik

  3. St.Petersburg State University and St.Petersburg Department of Steklov Institute of Mathematics, St.Petersburg, Russia

    F. V. Petrov

Authors
  1. A. M. Vershik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. V. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Vershik.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 507, 2021, pp. 15–25.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vershik, A.M., Petrov, F.V. A Generalized Maxwell–Poincaré Lemma and Wishart Measures. J Math Sci 261, 601–607 (2022). https://doi.org/10.1007/s10958-022-05774-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-05774-3

Search

Navigation