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Mixing Time Bounds via the Spectral Profile

   
@article{EJP300,
	author = {Sharad Goel and Ravi Montenegro and Prasad Tetali},
	title = {Mixing Time Bounds via the Spectral Profile},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {11},
	year = {2006},
	keywords = {},
	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.},
	pages = {no. 1, 1-26},
	issn = {1083-6489},
	doi = {10.1214/EJP.v11-300},    
        url = {http://ejp.ejpecp.org/article/view/300}}