The idea of writing up a book on the hydrodynamic behavior of interacting particle systems
was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the …

The aim of this book is to present some mathematical results describing the transition from
kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to …

The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

We introduce what we call the second-order Boltzmann–Gibbs principle, which allows one
to replace local functionals of a conservative, one-dimensional stochastic process by a …

We provide a rigorous derivation of the Brownian motion as the limit of a deterministic
system of hard-spheres as the number of particles NN goes to infinity and their diameter ε ε …

The addition of stochastic terms to a deterministic equation describing the time evolution of a
macroscopic physical system is often done in a heuristic intuitive way. However for …

We consider the quantum many-body dynamics at the weak-coupling scaling. We derive
rigorously the quantum Boltzmann equation, which contains the classical hard sphere model …

This is largely an attempt to provide probabilists some orientation to an important class of
non-linear partial differential equations in applied mathematics, the incompressible Navier …

Abstract We consider N*N Hermitian random matrices with independent identically
distributed entries (Wigner matrices). We assume that the distribution of the entries have a …

Invariance principles are proved under diffusive scaling for the centered position of a tagged
particle in the simple exclusion process with asymmetric nonzero drift jump probabilities in …