Thinking Probabilistically

Stochastic Processes, Disordered Systems, and Their Applications

Ariel Amir

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781108479523
• eBook ISBN: 9781108858878
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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

• Cover
• Half-title
• Title page
• Copyright information
• Contents
• Acknowledgments
• 1 Introduction
• 2 Random Walks
• 3 Langevin and Fokker–Planck Equations and Their Applications
• 4 Escape Over a Barrier
• 5 Noise
• 6 Generalized Central Limit Theorem and Extreme Value Statistics
• 7 Anomalous Diffusion
• 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