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