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 Electronic Journal of Probability > Vol. 11 (2006) > Paper 1 open journal systems 


Mixing Time Bounds via the Spectral Profile

Sharad Goel, Standford University, USA
Ravi Montenegro, University of Massachusetts Lowell, USA
Prasad Tetali, Georgia Institute of Technology, USA


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 Za x Zb, to obtain tight bounds on the corresponding mixing times.


Full text: PDF

Pages: 1-26

Published on: January 24, 2006
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Electronic Journal of Probability. ISSN: 1083-6489