The densities and distributions of the largest eigenvalue and the trace of a Beta

The densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix

Published:2019-12-03 Issue:01 Volume:10 Page:2150010
ISSN:2010-3263
Container-title:Random Matrices: Theory and Applications
language:en
Short-container-title:Random Matrices: Theory Appl.

Author:

Drensky Vesselin¹,Edelman Alan²,Genoar Tierney³,Kan Raymond⁴,Koev Plamen³^ORCID

Affiliation:

1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

2. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

3. Department of Mathematics, San Jose State University, 1 Washington Square, San Jose, CA 95192, USA

4. Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, Canada

Abstract

We present new expressions for the densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix. The series expansions for these expressions involve fewer terms than previously known results. For the trace, we also present a new algorithm that is linear in the size of the matrix and the degree of truncation, which is optimal.

Funder

National Science Foundation

San Jose State University

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S2010326321500106

Reference13 articles.

1. Accurate and efficient evaluation of Schur and Jack functions

2. Asymptotics for Products of Characteristic Polynomials in Classical β-Ensembles

3. THE BETA-MANOVA ENSEMBLE WITH GENERAL COVARIANCE

4. The beta-Wishart ensemble