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arXiv · 1610.08561

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

Alfredo Deaño·Nick Simm
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Abstract

In this paper, we compute the probability that an $N \times N$ matrix from the generalised Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar \cite{DM}. 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.

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Alfredo Deaño, Nick Simm. 2016-10-26. On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials. https://doi.org/10.1016/j.jat.2017.04.004

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