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· 제목 : Markov Chains and Mixing Times (Hardcover)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470429621
· 쪽수 : 464쪽
· 출판일 : 2017-11-17
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470429621
· 쪽수 : 464쪽
· 출판일 : 2017-11-17
목차
- Basic methods and examples: Introduction to finite Markov chains
- Classical (and useful) Markov chains
- Markov chain Monte Carlo: Metropolis and Glauber chains
- Introduction to Markov chain mixing
- Coupling
- Strong stationary times
- Lower bounds on mixing times
- The symmetric group and shuffling cards
- Random walks on networks
- Hitting times
- Cover times
- Eigenvalues
- The plot thickens: Eigenfunctions and comparison of chains
- The transportation metric and path coupling
- The Ising model
- From shuffling cards to shuffling genes
- Martingales and evolving sets
- The cutoff phenomenon
- Lamplighter walks
- Continuous-time chains
- Countable state space chains
- Monotone chains
- The exclusion process
- Cesaro mixing time, stationary times, and hitting large sets
- Coupling from the past
- Open problems
- Background material
- Introduction to simulation
- Ergodic theorem
- Solutions to selected exercises
- Bibliography
- Notation index
- Index.
