Books written by Yakov G. Sinai.

Yakov Sinai won the Abel Prize in 2014 for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.

Theory of Probability and Random Processes

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory.

Probability Theory: An Introductory Course

Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners.

Topics in Ergodic Theory

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems.

Selecta I: Ergodic Theory and Dynamical Systems

The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups.

Selecta II: Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics

The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability.

Selecta III: Professor Sinai's Selected Papers

Russian Mathematicians in the 20th Century

In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians.

Dynamical Systems: A Collection of Papers

This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.