4 papers
Regularity of solutions of the Dyson equation and applications
Valentin Pesce
The goal of this short paper is to investigate the regularity of the solutions of the Dyson equation. In the work of Bertucci and al. [3, 4, 5], a new notion of solutions for the D…
Improved well-posedness for the limit flow of differentiation of roots of polynomials
Charles Bertucci, Valentin Pesce
In this paper, we study the partial differential equation on the circle that was heuristically obtained by Steinerberg [32] on the real line and which represents the evolution of t…
From random matrices to systems of particles in interaction
Valentin Pesce
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of partic…
A new approach for the unitary Dyson Brownian motion through the theory of viscosity solutions
Charles Bertucci, Valentin Pesce
In this paper, we study the unitary Dyson Brownian motion through a partial differential equation approach recently introduced for the real Dyson case. The main difference with the…