In this introductory chapter we discuss some basic approaches to modeling of stochastic
optimization problems. We start with motivating examples and then proceed to formulation of …

We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …

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 …

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 …

This is a substantial revision of the previous edition with added new material. The
presentation of Chapter 6 is updated. In particular the Interchangeability Principle for risk …

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 idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

Score-based generative modeling (SGM) is a highly successful approach for learning a
probability distribution from data and generating further samples. We prove the first …

Includes material for a standard graduate class, advanced material not covered by the
standard course but necessary in order to read research literature in the area, and extensive …

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 …