Deaño, Alfredo and Simm, Nick (2017) On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials. Journal of Approximation Theory, 219 . pp. 44-59. ISSN 0021-9045.

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Abstract

In this paper, we compute the probability that an N × N matrix from the generalised Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar [15]. For this purpose, we work out the large degree asymptotics of semi-classical Laguerre polynomials and their recurrence coefficients, using the steepest descent analysis of the corresponding Riemann–Hilbert problem.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Matrix analytic methods, Laguerre polynomials , Riemann-Hilbert problems
Journal or Publication Title:	Journal of Approximation Theory
Publisher:	Elsevier
ISSN:	0021-9045
Official Date:	August 2017
Dates:	Date Event August 2017 Published 6 May 2017 Available 25 April 2017 Accepted 27 October 2016 Submitted
Volume:	219
Page Range:	pp. 44-59
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	17 May 2017
Funder:	Spain. Ministerio de Economía y Competitividad [Ministry of Economy and Competitiveness] (MINECO), Leverhulme Trust (LT)
Grant number:	MTM2012-36732-C03-01, MTM2012-3478 (MINECO), ECF-2014-309 (Leverhulme Trust (LT))

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