The compact text covers mathematical basics, probability, brownian motion and stationary stochastic processes, before introducing statistical mechanics and applying these techniques to both equilibrium and time-dependent situations. The classic Ising model is dealt with, before addressing more advanced time-dependent problems including memory. Feymann diagrams are used to illustrate the solution of the heat equation with a potential. It contains a straightforward discussion of the Langevin/Ornstein-Uhlenbeck equation and its relationship with the Fokker-Planck equation that might allow this book to be used as background reading for more financially orientated courses.
Who is it for? Undergraduate (fourth year) or, more likely, postgraduate mathematicians or theoretical physicists with an interest in interdisciplinary mathematics.
Presentation Condensed and fast-paced, the main text is only 159 pages long. Each chapter concludes with a raft of exercises.
Would you recommend it? Yes, as a good lecture text for advanced students with an interest in interdisciplinary applications.
Stochastic Tools in Mathematics and Science
Authors Alexandre J. Chorin, Ole H Hald