Markov Chains and Mixing Times 1st Edition by David A. Levin (PDF)

Description

This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This beautiful undergraduate textbook is a labor of love. It introduces modern topics, starting from using couplings to determine mixing times, and going all the way to current trends and topics such as Wilson’s algorithm and coupling from the past. It’s notable just for introducing students to coupling at this early stage! Its amazingly written in the American undergraduate style. It’s intended to be used. It could be used as a replacement for Stochastic Processes, but its better to have both in the curriculum. Many computer science departments have a course on Markov chain methods which has strong overlap. I had students doing independent study from it (a preprint version) from math, stats and finance-econ. The book is appropriate for self-study for students.

⭐Book is new and no damage. The print quality is good.

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