Thinking Probabilistically: Stochastic Processes, Disordered Systems, and Their

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Thinking Probabilistically by Ariel Amir

Assuming only an undergraduate-level background in mathematics, this book explains the power of thinking probabilistically through a diverse set of applications drawn from science. It covers a wide range of topics never before discussed together in a unified fashion while keeping technicalities to a minimum.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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.

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.

Review

'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 Lévy-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
'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

Promotional

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

Review Quote

'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 L

Promotional \"Headline\"

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

Description for Bookstore

Assuming only an undergraduate-level background in mathematics, this book explains the power of thinking probabilistically through a diverse set of applications drawn from science. It covers a wide range of topics never before discussed together in a unified fashion while keeping technicalities to a minimum.

Description for Library

Assuming only an undergraduate-level background in mathematics, this book explains the power of thinking probabilistically through a diverse set of applications drawn from science. It covers a wide range of topics never before discussed together in a unified fashion while keeping technicalities to a minimum.

Details ISBN1108479529 Author Ariel Amir Short Title Thinking Probabilistically Publisher Cambridge University Press Language English Year 2020 ISBN-10 1108479529 ISBN-13 9781108479523 Format Hardcover Pages 242 Publication Date 2020-12-17 DEWEY 519.2 UK Release Date 2020-12-17 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom AU Release Date 2020-12-17 NZ Release Date 2020-12-17 Illustrations Worked examples or Exercises Subtitle Stochastic Processes, Disordered Systems, and Their Applications Alternative 9781108789981 Audience Tertiary & Higher Education Country of Origin US Product Class Description Mathematics
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