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Mixing Time Bounds via the Spectral Profile


 
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1. Title Title of document Mixing Time Bounds via the Spectral Profile
 
2. Creator Author's name, affiliation, country Sharad Goel; Standford University, USA
 
2. Creator Author's name, affiliation, country Ravi Montenegro; University of Massachusetts Lowell, USA
 
2. Creator Author's name, affiliation, country Prasad Tetali; Georgia Institute of Technology, USA
 
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4. Description Abstract On complete, non-compact manifolds and infinite graphs, Faber-Krahn inequalities have been used to estimate the rate of decay of the heat kernel. We develop this technique in the setting of finite Markov chains, proving upper and lower $L^{\infty}$ mixing time bounds via the spectral profile. This approach lets us recover and refine previous conductance-based bounds of mixing time (including the Morris-Peres result), and in general leads to sharper estimates of convergence rates. We apply this method to several models including groups with moderate growth, the fractal-like Viscek graphs, and the product group $Z_a \times Z_b$, to obtain tight bounds on the corresponding mixing times.
 
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7. Date (YYYY-MM-DD) 2006-01-24
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/300
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-300
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
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