Cheeger bound

In mathematics, the Cheeger bound is a bound of the second largest eigenvalue of the transition matrix of a finite-state, discrete-time, reversible stationary Markov chain.

It can be seen as a special case of Cheeger inequalities in expander graphs.

be a finite set and let

be the transition probability for a reversible Markov chain on

Assume this chain has stationary distribution

acting on the space of functions from

The Cheeger bound is a bound on the second largest eigenvalue

Theorem (Cheeger bound):

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