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Thinking Probabilistically

Thinking Probabilistically
Stochastic Processes, Disordered Systems, and Their Applications

$49.99 (P)

  • Author: Ariel Amir, Harvard University, Massachusetts
  • Publication planned for: February 2021
  • availability: Not yet published - available from February 2021
  • format: Paperback
  • isbn: 9781108789981

$ 49.99 (P)

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About the Authors
  • 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
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    Reviews & endorsements

    ‘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

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    Product details

    • Publication planned for: February 2021
    • format: Paperback
    • isbn: 9781108789981
    • dimensions: 244 x 170 mm
    • availability: Not yet published - available from February 2021
  • 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...

  • Author

    Ariel Amir, Harvard University, Massachusetts
    Ariel Amir is a Professor at Harvard University, Massachusetts. His research centers on the theory of complex systems.

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