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

ISBN-13: 9781493997886 / Angielski / Miękka / 2019 / 514 str.

Yakov G. Sinai

Opis

This book collects 20 papers that span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields.

Recenzje

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)

Spis treści

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.

Blurb

​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 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 2012e)