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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]

Sharad Goel coauthored a method for estimating mixing time of a Markov chain through the spectral profile, with Ravi Montenegro and Prasad Tetali. Their analysis gives upper and lower convergence bounds and applies them to several families of graphs. The central mechanism is to track how relaxation changes with the stationary mass of a function's support.^[ref]