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2006 Mixing Time Bounds via the Spectral Profile
Sharad Goel, Ravi Montenegro, Prasad Tetali
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Electron. J. Probab. 11: 1-26 (2006). DOI: 10.1214/EJP.v11-300


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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Sharad Goel. Ravi Montenegro. Prasad Tetali. "Mixing Time Bounds via the Spectral Profile." Electron. J. Probab. 11 1 - 26, 2006.


Accepted: 24 January 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1109.60061
MathSciNet: MR2199053
Digital Object Identifier: 10.1214/EJP.v11-300

Vol.11 • 2006
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