Levin, David Asher 1971
Overview
Works:  2 works in 10 publications in 1 language and 296 library holdings 

Genres:  Dissertations, Academic 
Roles:  Author 
Classifications:  QA274.7, 519.233 
Publication Timeline
.
Most widely held works by
David Asher Levin
Markov chains and mixing times
by
David Asher Levin(
Book
)
8 editions published between 2008 and 2009 in English and held by 290 WorldCat member libraries worldwide
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
8 editions published between 2008 and 2009 in English and held by 290 WorldCat member libraries worldwide
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
Phase transitions in probability percolation and hidden Markov models
by
David Asher Levin(
)
2 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
We investigate combinatorial probability structures which exhibit phase transitions. The simplest and most widely studied such model is Bernoulli percolation on the lattices Zd, for d ≥ 2. We investigate the geometry of infinite percolation clusters on Zd when d ≥ 3, characterizing which flows these clusters can support. We also study a class of hidden Markov models first proposed by Harris and Keane [HK97]. We prove that in many cases, the model exhibits an unexpected phase transition. Finally, we study a generalization of the HarrisKeane model when the underlying Markov chain is random walk on Z. This model is a noisy version of the random walks on scenery studied by Benjamini and Kesten [BK96] and Howard [How96a, How96b]
2 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
We investigate combinatorial probability structures which exhibit phase transitions. The simplest and most widely studied such model is Bernoulli percolation on the lattices Zd, for d ≥ 2. We investigate the geometry of infinite percolation clusters on Zd when d ≥ 3, characterizing which flows these clusters can support. We also study a class of hidden Markov models first proposed by Harris and Keane [HK97]. We prove that in many cases, the model exhibits an unexpected phase transition. Finally, we study a generalization of the HarrisKeane model when the underlying Markov chain is random walk on Z. This model is a noisy version of the random walks on scenery studied by Benjamini and Kesten [BK96] and Howard [How96a, How96b]
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Associated Subjects