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By Sharad Goel, Ravi Montenegro, Prasad Tetali.

Author-hosted primary paper; arXiv:math/0505690 (2005). Section 1.2, Definitions 1.4–1.5 define the variance-normalized spectral profile. Section 2.2, Definition 2.2 and Lemma 2.4 compare it with the conductance profile. Section 1.1 defines stationary reversibility.

Prasad Tetali coauthored the spectral profile method for bounding mixing time of a Markov chain with Sharad Goel and Ravi Montenegro. It refines a single spectral gap by considering functions supported on sets of different stationary masses. This makes the geometry of small sets useful for quantifying convergence to the stationary distribution.^[ref]

Ravi Montenegro contributed, with Sharad Goel and Prasad Tetali, to bounds on mixing time of a Markov chain using the spectral profile. Their approach adapts Faber-Krahn inequalities to finite Markov chains and compares the resulting bounds with conductance of a Markov chain methods. It captures information at multiple set sizes that a single bottleneck estimate can miss.^[ref]