Yakov G Sinai - Böcker

From the reviews:“The first volume is devoted to ergodic theory and dynamical systems. The reader will also have a touch of Sinai’s personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results.” (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)

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

This book contains several contributions on the most outstanding events in the development of 20th century mathematics, representing a wide variety of specialities in which Russian and Soviet mathematicians played a considerable role. The articles are written in an informal style, from mathematical philosophy to the description of the development of ideas, personal memories and give a unique account of personal meetings with famous mathematicians of 20th century mathematics who exerted great influence in its development. This book will be of great interest to mathematicians, who will enjoy seeing their own specialities described with some historical perspective. Historians will read it with the same motive, and perhaps also to select topics for future investigation.

The book consists of two parts. The first part concerns the classical probability theory. It contains a detailed analysis of Markov chains, Limit theorems, their relation to Renormalization Group theory. It also describes several applications of probability theory, which are not discussed in most other text-books. The second part includes the theory of stationary random processes, martingales, stochastic integrals and stochastic differential equations. One section is devoted to the theory of Gibbs random fields. The book contains essential material for an undergraduate or a graduate course in Probability theory and the theory of Random Processes. It may also serve as a reference for scientists who use modern probability theory in their research.

Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics.In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.