As a counterpoint to classical stochastic particle methods for linear diffusion equations, such
as Langevin dynamics for the Fokker-Planck equation, we develop a deterministic particle …

We have developed a new class of generative algorithms capable of efficiently learning
arbitrary target distributions from possibly scarce, high-dimensional data and subsequently …

We study weighted porous media equations on domains $\Omega\subseteq {\mathbb R}^ N
$, either with Dirichlet or with Neumann homogeneous boundary conditions when …

This paper is devoted to the study of probability measures with heavy tails. Using the
Lyapunov function approach we prove that such measures satisfy different kind of functional …

Lipschitz regularized f-divergences are constructed by imposing a bound on the Lipschitz
constant of the discriminator in the variational representation. These divergences interpolate …

We prove existence and uniqueness of solutions to a class of porous media equations
driven by the fractional Laplacian when the initial data are positive finite Radon measures …

The time decay of fully discrete finite-volume approximations of porous-medium and
fastdiffusion equations with Neumann or periodic boundary conditions is proved in the …

In this expository work we discuss the asymptotic behaviour of the solutions of the classical
heat equation posed in the whole Euclidean space. After an introductory review of the main …

The goal of this paper is to give a non-local sufficient condition for generalized Poincaré
inequalities which extends the well-known Bakry-Emery condition. Such generalized …

This paper presents different approaches, based on functional inequalities, to study the
speed of convergence in total variation distance of ergodic diffusion processes with initial …