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

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.

Citation

Download Citation

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

Information

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

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.11 • 2006
Back to Top