Selecta II: Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics (Hardcover, 2010)

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 Schrodinger 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.