Probabilistic inequalities | Stochastic processes | Statistical inequalities

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. Let be a finite set and let be the transition probability for a reversible Markov chain on . Assume this chain has stationary distribution . Define and for define Define the constant as The operator acting on the space of functions from to , defined by has eigenvalues . It is known that . The Cheeger bound is a bound on the second largest eigenvalue . Theorem (Cheeger bound): (Wikipedia).

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From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie

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From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie

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From playlist Science Unplugged: General Relativity

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Stochastic matrix | Cheeger constant | Mathematics | Stationary distribution | Expander graph | Markov chain