Random Processes in Physics

Covering foundational concepts to advanced applications, Random Processes in Physics is designed for physics undergraduates exploring probability theory.

This concise book stands out by covering topics that range from the foundational aspects of probability theory to its applications in fields such as equilibrium statistical physics, quantum theory, and complex systems. The primary goal of Random Processes in Physics is to present probabilistic concepts in a manner that is accessible for physics undergraduates, while keeping practical applications in physics at the forefront of discussion.

The book is organized into three distinct parts. Part I, titled 'Fundamentals,' introduces the essential concepts of probability theory, including the motivations behind the study of probabilities, the challenges encountered when working with them, and several basic examples. This section also delves into the mathematical concepts that underpin probability theory, joint probabilities, and Bayes' theorem. Additionally, it addresses how computers generate (pseudo-)random numbers, a crucial topic for modern physicists.

Part II focuses on 'Specific Probability Distributions,' discussing those most relevant to physics applications, such as the Central Limit Theorem, Gaussian distributions, and Poissonian distributions. The exploration extends to Levy flights, self-similarity, power law distributions, and extreme value statistics. Finally, Part III, 'Applications in and Beyond Physics,' examines the application of random process modeling in physics and related disciplines, emphasizing quantum theory and classical statistical physics through the lens of information theory. This comprehensive approach ensures that Random Processes in Physics is suitable for undergraduate students in their early years of study.