{"product_id":"markov-chains-and-mixing-times-9781470429621","title":"Markov Chains and Mixing Times","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOffers an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises and citations to important research papers it makes an outstanding basis for either a lecture course or self-study.” — David Aldous, University of California, Berkeley\u003cbr\u003e\u003cbr\u003e”Mixing time is the key to Markov chain Monte Carlo, the queen of approximation techniques. With new chapters on monotone chains, exclusion processes, and set-hitting, \u003cem\u003eMarkov Chains and Mixing Times\u003c\/em\u003e is more comprehensive and thus more indispensable than ever. Prepare for an eye-opening mathematical tour!” — Peter Winkler, Dartmouth College\u003cbr\u003e\u003cbr\u003e”The study of finite Markov chains has recently attracted increasing interest from a variety of researchers. This is the second edition of a very valuable book on the subject. The main focus is on the mixing time of Markov chains, but there is a lot of additional material. In this edition, the authors have taken the opportunity to add new material and bring the reader up to date on the latest research. I have used the first edition in a graduate course and I look forward to using this edition for the same purpose in the near future.” — Alan Frieze, Carnegie Mellon University\u003cbr\u003e\u003cbr\u003ePraise for the first edition:\u003cbr\u003e\u003cbr\u003e”\u003cem\u003eMarkov Chains and Mixing Times\u003c\/em\u003e is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement.” — Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University\u003cbr\u003e\u003cbr\u003e”In this book, [the authors] rapidly take a well-prepared undergraduate to the frontiers of research. Short, focused chapters with clear logical dependencies allow readers to use the book in multiple ways.” — \u003cem\u003eCHOICE Magazine\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eBasic methods and examples: Introduction to finite Markov chains\u003c\/li\u003e\n\u003cli\u003eClassical (and useful) Markov chains\u003c\/li\u003e\n\u003cli\u003eMarkov chain Monte Carlo: Metropolis and Glauber chains\u003c\/li\u003e\n\u003cli\u003eIntroduction to Markov chain mixing\u003c\/li\u003e\n\u003cli\u003eCoupling\u003c\/li\u003e\n\u003cli\u003eStrong stationary times\u003c\/li\u003e\n\u003cli\u003eLower bounds on mixing times\u003c\/li\u003e\n\u003cli\u003eThe symmetric group and shuffling cards\u003c\/li\u003e\n\u003cli\u003eRandom walks on networks\u003c\/li\u003e\n\u003cli\u003eHitting times\u003c\/li\u003e\n\u003cli\u003eCover times\u003c\/li\u003e\n\u003cli\u003eEigenvalues\u003c\/li\u003e\n\u003cli\u003eThe plot thickens: Eigenfunctions and comparison of chains\u003c\/li\u003e\n\u003cli\u003eThe transportation metric and path coupling\u003c\/li\u003e\n\u003cli\u003eThe Ising model\u003c\/li\u003e\n\u003cli\u003eFrom shuffling cards to shuffling genes\u003c\/li\u003e\n\u003cli\u003eMartingales and evolving sets\u003c\/li\u003e\n\u003cli\u003eThe cutoff phenomenon\u003c\/li\u003e\n\u003cli\u003eLamplighter walks\u003c\/li\u003e\n\u003cli\u003eContinuous-time chains\u003c\/li\u003e\n\u003cli\u003eCountable state space chains\u003c\/li\u003e\n\u003cli\u003eMonotone chains\u003c\/li\u003e\n\u003cli\u003eThe exclusion process\u003c\/li\u003e\n\u003cli\u003eCesaro mixing time, stationary times, and hitting large sets\u003c\/li\u003e\n\u003cli\u003eCoupling from the past\u003c\/li\u003e\n\u003cli\u003eOpen problems\u003c\/li\u003e\n\u003cli\u003eBackground material\u003c\/li\u003e\n\u003cli\u003eIntroduction to simulation\u003c\/li\u003e\n\u003cli\u003eErgodic theorem\u003c\/li\u003e\n\u003cli\u003eSolutions to selected exercises\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eNotation index\u003c\/li\u003e\n\u003cli\u003eIndex.\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046670438743,"sku":"9781470429621","price":66.6,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470429621.jpg?v=1740271804","url":"https:\/\/bookcurl.com\/products\/markov-chains-and-mixing-times-9781470429621","provider":"Book Curl","version":"1.0","type":"link"}