Electronic Journal of Probability

Mixing Time Bounds via the Spectral Profile

Sharad Goel, Ravi Montenegro, and Prasad Tetali

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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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Electron. J. Probab., Volume 11 (2006), paper no. 1, 1-26.

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

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Goel, Sharad; Montenegro, Ravi; Tetali, Prasad. Mixing Time Bounds via the Spectral Profile. Electron. J. Probab. 11 (2006), paper no. 1, 1--26. doi:10.1214/EJP.v11-300. https://projecteuclid.org/euclid.ejp/1464730536

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