Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
Faster random generation of linear extensions
Discrete Mathematics - Special issue on partial ordered sets
Markov Chain Algorithms for Planar Lattice Structures
SIAM Journal on Computing
Spectral Gap and log-Sobolev Constant for Balanced Matroids
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Sampling adsorbing staircase walks using a new Markov chain decomposition method
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Factoring graphs to bound mixing rates
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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Markov chain decomposition is a tool for analysing the convergence rate of a complicated Markov chain by studying its behaviour on smaller, more manageable pieces of the state space. Roughly speaking, if a Markov chain converges quickly to equilibrium when restricted to subsets of the state space, and if there is sufficient ergodic flow between the pieces, then the original Markov chain also must converge rapidly to equilibrium. We present a new version of the decomposition theorem where the pieces partition the state space, rather than forming a cover where pieces overlap, as was previously required. This new formulation is more natural and better suited to many applications. We apply this disjoint decomposition method to demonstrate the efficiency of simple Markov chains designed to uniformly sample circuits of a given length on certain Cayley graphs. The proofs further indicate that a Markov chain for sampling adsorbing staircase walks, a problem arising in statistical physics, is also rapidly mixing.