This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

High-dimensional probability offers insight into the behavior of random vectors, random
matrices, random subspaces, and objects used to quantify uncertainty in high dimensions …

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 …

Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …

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 …

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 observation of the concentration of measure phenomenon is inspired by isoperimetric
inequalities. This book offers the basic techniques and examples of the concentration of …

Now back in print by the AMS, this is a significantly revised edition of a book originally
published in 1987 by Academic Press. This book gives the reader an introduction to the …

This text provides a systematic exposition of the modern theory of Gaussian measures. It
presents, with complete and detailed proofs, fundamental facts about finite and infinite …

This article gives a detailed account of recent investigations of weak elliptic and parabolic
equations for measures with unbounded and possibly singular coefficients. The existence …