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Extreme points of the Vandermonde determinant and Wishart ensemble on symmetric cones
Department of Mathematics, Busitema University, Tororo, Uganda.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-3204-617X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
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2022 (English)In: Springer Proceedings in Mathematics and Statistics / [ed] Anatoliy Malyarenko, Ying Ni, Milica Rančić, Sergei Silvestrov, Springer Nature, 2022, Vol. 408, p. 625-649Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we demonstrate the extreme points of the Wishart joint eigenvalue probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The extreme of points of theVandermonde4 determinant are defined to be a set of boundary points of the symmetric cones that occur in both the discrete and continuous part of the Gindikin set. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart ensembles in Herm(m,C), Herm(m,H), Herm(3,O) denoting respectively the Jordan algebra of all Hermitian matrices of size m × m with complex entries, the skew field H of quaternions, and the algebra O of octonions.

Place, publisher, year, edition, pages
Springer Nature, 2022. Vol. 408, p. 625-649
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 408
Keywords [en]
Jordan algebras, Vandermonde determinant, Symmetric cones, Wishart joint eigenvalue distributions
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-61410DOI: 10.1007/978-3-031-17820-7_27Scopus ID: 2-s2.0-85171539089ISBN: 978-3-031-17819-1 (print)OAI: oai:DiVA.org:mdh-61410DiVA, id: diva2:1722913
Conference
SPAS 2019, Västerås, Sweden, September 30–October 2
Funder
Sida - Swedish International Development Cooperation AgencyAvailable from: 2023-01-01 Created: 2023-01-01 Last updated: 2023-10-04Bibliographically approved

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Publisher's full textScopushttps://link.springer.com/book/9783031178191

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Malyarenko, AnatoliyLundengård, KarlSilvestrov, Sergei

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Citation style
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