Selecta II, 2010 Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics

Langue : Anglais

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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)

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.

Sinai is one of the giants of modern mathematics Sinai is pioneer in building bridges between dynamical systems and statistical mechanics community with seminal papers in this area Commentary provided by Sinai after each paper Includes supplementary material: sn.pub/extras