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Informatics Report Series
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| Title:Elementary bounds on Poincar and log-Sobolev constants for decomposable Markov chains |
| Authors:
Mark Jerrum
; Jung-Bae Son
; Prasad Tetali
; Eric Vigoda
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| Date: 2004 |
| Publication Title:Annals of Applied Probability |
| Publisher:The Institute of Mathematical Statistics |
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Publication Type:Journal Article
Publication Status:Published
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Volume No:14(4)
Page Nos:1741-1765
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DOI:10.1214/105051604000000639
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- Abstract:
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We consider finite-state Markov chains that can be naturally decomposed into smaller ``projection'' and ``restriction'' chains. Possibly this decomposition will be inductive, in that the restriction chains will be smaller copies of the initial chain. We provide expressions for Poincare (resp. log-Sobolev) constants of the initial Markov chain in terms of Poincare (resp. log-Sobolev) constants of the projection and restriction chains, together with further a parameter. In the case of the Poincare constant, our bound is always at least as good as existing ones and, depending on the value of the extra parameter, may be much better. There appears to be no previously published decomposition result for the log-Sobolev constant. Our proofs are elementary and self-contained.
- Links To Paper
- 1st Link
- Bibtex format
- @Article{EDI-INF-RR-0476,
- author = {
Mark Jerrum
and Jung-Bae Son
and Prasad Tetali
and Eric Vigoda
},
- title = {Elementary bounds on Poincar and log-Sobolev constants for decomposable Markov chains},
- journal = {Annals of Applied Probability},
- publisher = {The Institute of Mathematical Statistics},
- year = 2004,
- volume = {14(4)},
- pages = {1741-1765},
- doi = {10.1214/105051604000000639},
- url = {http://front.math.ucdavis.edu/math.PR/0503537},
- }
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