Article

While it is known that propagation of chaos holds at rate $O(1/N)$ uniformly in time, and Gibbs relaxation at rate $O(e^{-ct})$ uniformly in $N$, we go a step further by showing that the cross error between chaos propagation and Gibbs relaxation is $O(N^{-1}e^{-ct})$.

Jul 31, 2025

We establish the conditional convex order and increasing convex order for McKean-Vlasov equations with common noise. Applications to stochastic control are also discussed.

Apr 24, 2025

We establish a fine version of the so-called creation-of-chaos phenomenon':' in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy O(1/N) up to an error due solely to initial pair correlations.

Apr 14, 2025

We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation.

Jun 1, 2024

We consider a suspension of active rigid particles (swimmers) in a steady Stokes flow, using for simplicity a steady-state model where particles are distributed according to a stationary ergodic random process, and we study its homogenization in the macroscopic limit. An analysis in the dilute regime shows that the activity of the particles can either increase or decrease the effective viscosity (depending on the swimming mechanism), in a way that strongly differs from the well-known effect of passive suspensions.

Mar 1, 2023

This report was written as a detailed abstract for the presentation I gave during the Arbeitsgemeinschaft: Quantitative Stochastic Homogenization, organized by A. Gloria and F. Otto in Oberwolfach in October 2022.

Nov 1, 2022

This is the manuscript of my PhD thesis. Some slides are also available, from which the image above, taken from the simulation of the evolution of 5000 particles in a star-shaped domain following a free-transport evolution with boundary effects, is extracted (I advise to open the pdf with Adobe, as embedded simulations work better there).

Dec 18, 2020