Lecturer:
Course Type:
PhD Course
Academic Year:
2024-2025
Period:
March - May
Duration:
50 h
Description:
Topics:
-
definition and basic properties of determinantal point processes;
-
short introduction to the theory of orthogonal polynomials;
-
unitary ensembles of random matrices.
-
Gaussian Unitary Ensemble. Semicircle law and local properties of the eigenvalues (sine-kernel and Airy-kernel processes). Asymptotic analysis of integrals.
-
Equilibrium measures. Connection between the density of zeros of orthogonal polynomials and eigenvalues of random matrices.
Main reference book:
P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Research Group: