On the probability of positive-definiteness in the gGUE via   semi-classical Laguerre polynomials
  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. 
Alfredo Dea\~no and Nick Simm
math-ph math.CA math.MP