The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

The objective of molecular dynamics computations is to infer macroscopic properties of
matter from atomistic models via averages with respect to probability measures dictated by …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

The purpose of this book is to present various results and techniques from the theory of
stochastic processes and in particular diffusion processes that are useful in the study of …