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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Projections of orbital measures and quantum marginal problems
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by Benoît Collins and Colin McSwiggen
Trans. Amer. Math. Soc. 376 (2023), 5601-5640
DOI: https://doi.org/10.1090/tran/8931
Published electronically: May 23, 2023

Abstract:

This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn’s problem, the randomized Schur’s problem, and the orbital corners process. In this general setting, we prove integral formulae for the probability densities, establish some properties of the densities, and discuss connections to multiplicity problems in representation theory as well as to known results in the symplectic geometry literature. As applications, we show a number of results on marginal problems in quantum information theory and also prove an integral formula for restriction multiplicities.
References
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Bibliographic Information
  • Benoît Collins
  • Affiliation: Department of Mathematics, Kyoto University, Japan
  • MR Author ID: 710054
  • ORCID: 0000-0001-7061-6861
  • Email: collins@math.kyoto-u.ac.jp
  • Colin McSwiggen
  • Affiliation: Courant Institute of Mathematical Sciences, New York University
  • MR Author ID: 1177558
  • Email: csm482@nyu.edu
  • Received by editor(s): February 13, 2022
  • Received by editor(s) in revised form: January 16, 2023
  • Published electronically: May 23, 2023
  • Additional Notes: The work of the first author was supported by JSPS KAKENHI 17K18734 and 17H04823, as well as by Japan–France Integrated Action Program (SAKURA), grant number JPJSBP120203202. The work of the second author was supported by the National Science Foundation under grant number DMS 2103170, and by JST CREST program JPMJCR18T6.
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 5601-5640
  • MSC (2020): Primary 15B52, 81P45, 05E10
  • DOI: https://doi.org/10.1090/tran/8931
  • MathSciNet review: 4630755