The focus of this book is the large-scale statistical behavior of solutions of divergence-form
elliptic equations with random coefficients, which is closely related to the long-time …

In this paper, we consider a continuous description based on stochastic differential
equations of the popular particle swarm optimization (PSO) process for solving global …

Recently a continuous description of particle swarm optimization (PSO) based on a system
of stochastic differential equations was proposed by Grassi and Pareschi in [Math. Models …

We introduce two new concepts of convergence of gradient systems (Q, E _ ε, R _ ε)(Q, E ε,
R ε) to a limiting gradient system (Q, E _0, R _0)(Q, E 0, R 0). These new concepts are called …

In this chapter we survey some recent results on the global minimization of a non-convex
and possibly non-smooth high dimensional objective function by means of particle-based …

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining
is an important technique to reduce the dimensionality of the problem. We will study and …

We consider a system of interacting particles governed by the generalized Langevin
equation (GLE) in the presence of external confining potentials, singular repulsive forces, as …

Macroscopic equations arising out of stochastic particle systems in detailed balance (called
dissipative systems or gradient flows) have a natural variational structure, which can be …

We establish a quantified overdamped limit for kinetic Vlasov–Fokker–Planck equations with
nonlocal interaction forces. We provide explicit bounds on the error between solutions of that …

We investigate various versions of multi-dimensional systems involving many species,
modeling aggregation phenomena through nonlocal interaction terms. We establish a …