4 papers
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…
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…
The tangent space to the Wasserstein space: parallel transport and other applications
Charles Bertucci
We propose a new notion of the formal tangent space to the Wasserstein space at a given measure. Modulo an integrability condition, we say that this tangent space…
On the doubling of variables technique in first order Hamilton-Jacobi equations
Charles Bertucci, Giacomo Ceccherini Silberstein
In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuni…