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Decomposition Methods and Sampling Circuits in the Cartesian Lattice

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Mathematical Foundations of Computer Science 2001 (MFCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2136))

Abstract

Decomposition theorems are useful tools for bounding the convergence rates of Markov chains. The theorems relate the mixing rate of a Markov chain to smaller, derivative Markov chains, defined by a partition of the state space, and can be useful when standard, direct methods fail. Not only does this simplify the chain being analyzed, but it allows a hybrid approach whereby different techniques for bounding convergence rates can be used on different pieces. We demonstrate this approach by giving bounds on the mixing time of a chain on circuits of length 2n in ℤd.

Supported in part by NSF Grant No. CCR-9703206.

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Randall, D. (2001). Decomposition Methods and Sampling Circuits in the Cartesian Lattice. In: Sgall, J., Pultr, A., Kolman, P. (eds) Mathematical Foundations of Computer Science 2001. MFCS 2001. Lecture Notes in Computer Science, vol 2136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44683-4_8

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  • DOI: https://doi.org/10.1007/3-540-44683-4_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42496-3

  • Online ISBN: 978-3-540-44683-5

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