A Random Walk in Science (repost)

This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.).

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon.

"Entropy and Energy- a Universal Competition" is a students textbook as well as a scientific monograph. The concepts of entropy and energy embody the effects of random walk in a body and of deterministic strife respectively, and are therefore often in competition. The book gives instructive examples from elementary thermodynamics and physico-chemistry and extrapolates the notion to non-standard thermodynamic subjects like shape memory, dissipation of the earth's atmosphere, and sociology. The works of the thermodynamic pioneers are presented, in particular Clausius, Carathéodory, Boltzmann, Gibbs, and Planck. The laws of thermodynamics and their limitations are discussed; also the pertinacious Gibbs paradox. The reader has numerous possibilities to influence the programs and thus develop an understanding for the thermodynamic principles.

Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercises in this text over the course of many years while working on topics which interested him the most.