Singular Linear Statistics and PIII
Y. Chen (Imperial College London, UK)In the talk I will give a quick introduction to Random Matrix Ensembles and the "linear statistics", a random variable that frequently appears in the applications of random matrix theory. In the Hermitean case, and for a particular linear statistics, I will show that the recurrence coefficients of the associated orthogonal polynomials is a Painleve III. Asymptotics of the (scaled-) Hankel determinant is found through integration.