Mini courses : Deformations of orthogonal polynomials and point processes (2/2)

by Guilherme Silva (Universidade de São Paulo)

Monday 11 May 2026, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

In the study of moderate deviations within the stochastic six-vertex model and the eigenvalues of random matrices, a crucial role is played by a simple deformation formula. This formula connects the logarithmic derivative of the gap probability to a weighted trace of a deformed orthogonal polynomial kernel.

 

In the study of moderate deviations of the stochastic six-vertex model, and also of eigenvalues of random matrices, a key role is played by a simple deformation formula, relating the log derivative of the gap probability to a weighted trace of a deformation of the original orthogonal polynomial kernel. 

 

The formula itself follows from straightforward analytic arguments, but what does the involved deformed kernel mean probabilistically? The goal of these two lectures is to clarify exactly that. We will review the necessary theory of point processes to make probabilistic sense of the deformed kernel, and discuss recent results built around it.