Thinking probabilistically: stochastic processes, disordered systems, and their applications

Table of Contents
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.

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.

Explains the power of probability theory both as a conceptual framework and as a tool across mathematics and physics
Avoids using unnecessary technicalities, keeping the mathematical prerequisites to a minimum
Contains numerous and diverse examples of interdisciplinary applications of probability theory