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.
By:
Ariel Amir (Harvard University Massachusetts)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions:
Height: 250mm,
Width: 175mm,
Spine: 17mm
Weight: 550g
ISBN: 9781108479523
ISBN 10: 1108479529
Pages: 242
Publication Date: 17 December 2020
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Hardback
Publisher's Status: Active
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.
Ariel Amir is a Professor at Harvard University, Massachusetts. His research centers on the theory of complex systems.
Reviews for Thinking Probabilistically: Stochastic Processes, Disordered Systems, and Their Applications
'A remarkable demonstration that advanced topics need not be esoteric. Amir takes us through random walks on networks, extreme value statistics, Kramers theory, anomalous diffusion and other topics generally omitted from introductory texts, always rooting every discussion in applications of terrific current interest. I found the discussion of Levy-stable distributions especially insightful as a principled approach to the nonstandard walks that abound in contexts from biophysics to finance.' Philip C. Nelson, University of Pennsylvania
