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

Deano, Alfredo and Simm, Nicholas (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

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Abstract

In this paper, we compute the probability that an N x N matrix from the generalized Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar (2008). 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
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematical Physics Group
Depositing User: Nicholas Simm
Date Deposited: 12 Jun 2018 15:18
Last Modified: 02 Jul 2019 15:31
URI: http://sro.sussex.ac.uk/id/eprint/75908

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