arXiv subjects

Francesco Carlo De Vecchi

Publications and source records attributed to Francesco Carlo De Vecchi.

3 recordsLinked to original sources

arXiv2026

A criterion for proving entropy chaos on path space

A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by Carlen, which are characterized by infinitesimal characteristic pairs, that is, a time-marginal probability density and a current velocity field. A key property of this broad class is that the processes remain diffusions under time-reversal. We prove that, given a suitable bound on the relative entropy (with respect to the Wiener measure) and the weak convergence of both drifts and fixed-time marginal densities, strong entropy chaos at the process level is achieved in the infinite particle limit, provided the limit drift satisfies a specific regularity condition. This stochastic framework encompasses various singular interacting particle systems and their related asymptotic scenarios.

math.PR↗

arXiv2025

Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum random system is established. A splitting strategy allows us to decompose the random system into a space-discrete heat equation with a stochastic boundary condition, and a nonlinear and nonlocal space-discrete differential system coupled with the first one and with deterministic initial and boundary conditions. The convergence result is obtained by first establishing some a priori estimates for both space-discrete splitted variables and then exploiting compact embedding theorems for time-space Besov spaces on the positive lattice. The convergence of a fully discrete approximation of the random system is also discussed.

math.PR↗

arXiv2025

Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential

In this paper, we consider the defocusing Hartree NLS with white noise external potential on T^3 i.e. the Hartree NLS whose linear part is given by the Anderson Hamiltonian. A Strichartz-type estimate is established for the Anderson Hamiltonian using perturbative arguments and the local and global well-posedness of the NLS is considered with initial data in the domain and form-domain of the Anderson Hamiltonian under different regularity assumptions on the Hartree interaction. Furthermore, we establish the Anderson Hartree NLS as an effective equation describing many-body Bosonic systems and, in particular, we prove the convergence of the linear Schrödinger equation for the many body system to the BBGKY hierarchy for the Coulomb interaction.

math.AP↗