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Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels


 
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1. Title Title of document Sharp edge, vertex, and mixed Cheeger type inequalities for finite Markov kernels
 
2. Creator Author's name, affiliation, country Ravi Montenegro; University of Massachusetts Lowell
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Markov chain, evolving sets, Cheeger inequality, eigenvalues
 
3. Subject Subject classification 60J10
 
4. Description Abstract We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several previous Cheeger inequalities, including ones involving edge-expansion, vertex-expansion, and mixtures of both. A bound on the smallest eigenvalue also follows.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF-VIGRE grant at Georgia Tech
 
7. Date (YYYY-MM-DD) 2007-10-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1269
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1269
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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