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On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials

Deaño, Alfredo, SImm, Nicholas J (2017) On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials. Journal of Approximation Theory, 220 . pp. 44-59. ISSN 0021-9045. (doi:10.1016/j.jat.2017.04.004) (KAR id:58331)

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Abstract

In this paper, we compute the probability that an NxN matrix from the generalised Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar. 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: Article
DOI/Identification number: 10.1016/j.jat.2017.04.004
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Alfredo Deano Cabrera
Date Deposited: 02 Nov 2016 11:23 UTC
Last Modified: 16 Feb 2021 13:38 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/58331 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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