Thinking Probabilistically
Stochastic Processes, Disordered Systems, and Their Applications

An introductory text providing the reader with a thorough background to the rich world of applications of stochastic processes.

Ariel Amir (Author)

9781108789981, Cambridge University Press

Paperback / softback, published 17 December 2020

242 pages
24.3 x 17 x 1.5 cm, 0.44 kg

'The book is a suitable springboard for self-study because it introduces a wide variety of topics and contains many references to current work. In the classroom, the book can function either as the basis for a course in special topics or as a source of material to spice up more traditional statistical-mechanics courses … the methods for studying random phenomena introduced in Thinking Probabilistically will help readers understand reasoning techniques that may not be terribly familiar to physicists. Moreover, following the author's arguments is a rewarding intellectual exercise in its own right.' Rob de Ruyter, Physics Today

Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion – includes Markov processes and random walks, Langevin and Fokker–Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.

1. Introduction
2. Random walks
3. Langevin and Focker–Planck equations and their applications
4. Escape over a barrier
5. Noise
6. Generalized central limit theorem and extreme value statistics
7. Anomalous diff usion
8. Random matrix theory
9. Percolation theory
Appendix A. Review of basic probability concepts and common distributions
Appendix B. A brief linear algebra reminder, and some Gaussian integrals
Appendix C. Contour integration and Fourier transform refresher
Appendix D. Review of Newtonian mechanics, basic statistical mechanics and Hessians
Appendix E. Minimizing functionals, the divergence theorem and saddle point approximations
Appendix F. Notation, notation...
References
Index.

Subject Areas: Stochastics [PBWL], Mathematical modelling [PBWH], Probability & statistics [PBT]