The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997). He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.This volume follows Volume I.
From the reviews:
"The second volume covers statistical mechanics and related topics. It contains 22 papers divided into four groups: Part I: Probability Theory; Part II: Statistical Mechanics; Part III: Mathematical Physics; Part IV: Mathematical Fluid Dynamics. The volume represents Sinai's work on the above topics spanning almost 40 years:the earliest paper is dated 1972, and the latest 2008. The choice of papers was made by Sinai himself, and he provides commentary for each one. The reader will ?nd a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. 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 2012e)
Reviews / Votes
From the reviews:
"The second volume covers statistical mechanics and related topics. It contains 22 papers divided into four groups . . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. 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)
Series
Edition
Language
Place of publication
Target group
Professional and scholarly
Illustrations
11 s/w Abbildungen, 53 farbige Abbildungen
XX, 514 p. 64 illus., 53 illus. in color. With New printing in a different form.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 29 mm
Weight
ISBN-13
978-1-4939-9788-6 (9781493997886)
DOI
10.1007/978-1-4419-6205-8
Schweitzer Classification
YAKOV SINAI has been a professor at Princeton University since 1993. He was educated at Moscow State University, and was a professor there till 1993.
Since 1971 he has also held the position of senior researcher at the Landau Institute of Theoretical Physics. He is known for fundamental work on dynamical systems, probability theory, mathematical physics, and statistical mechanics. He has been awarded, among other honors, the Boltzmann Medal (in 1986) and Wolf Prize in Mathematics (in 1997). He is a member of Russian and American Academies of Sciences.
LEONID KORALOV is an assistant professor at the University of Maryland. From 2000 till 2006 he was an assistant professor at Princeton University, prior to which he worked at the Institute for Advanced Study in Princeton. He did his undergraduate work at Moscow State University, and got his PhD from SUNY at Stony Brook in 1998. He works on problems in the areas of homogenization, diffusion processes, and partial differential equations.
Probability Theory.- Simple Random Walks on Tori.- The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium.- A remark concerning random walks with random potentials.- A Random Walk with Random Potential.- Distribution of Some Functionals of the Integral of a Random Walk.- Statistical Mechanics.- Construction of Dynamics in One-Dimensional Systems of Statistical Mechanics.- Phase Diagrams of Classical Lattice Systems.- An Analysis of ANNNI Model by Peierl's Contour Method.- Critical Indices for Dyson's Asymptotically-Hierarchical Models.- Investigation of the Critical Point in Models of the Type of Dyson's Hierarchical Models.- Mathematical Physics.- The One-Dimensional Schrödinger Equation with a Quasiperiodic Potential.- Distribution of Energy Levels of Quantum Free Particle on the Liouville Surface and Trace Formulae.- Mathematical Problems in the Theory of Quantum Chaos.- Dynamics of a Heavy Particle Surrounded by a Finite Number of Light Particles.- Adiabatic Piston as a Dynamical System.- Poisson Distribution in a Geometric Problem.- Mathematical Fluid Dynamics.- Invariant measures for Burgers equation with stochastic forcing.- An Elementary Proof of the Existence and Uniqueness Theorem for the Navier-Stokes Equations.- Statistics of Shocks in Solutions of Inviscid Burgers Equation.- Gibbsian Dynamics and Ergodicity for the Stochastically Forced Navier-Stokes Equation.- Blow Ups of Complex Solutions of the 3D-Navier-Stokes System and Renormalization Group Method.- Two Results Concerning Asymptotic Behavior of Solutions of the Burgers Equation with Force.
