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Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model

Pierre MATHIEU·Pierre PICCO
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Abstract

We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We derive upper bounds for the time to reach the equilibrium. As an example of application we consider a special case of finite state Markov process in random environment: the Metropolis dynamics of the Random Energy Model. We also study the process of the environment as seen from the process.

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Pierre MATHIEU, Pierre PICCO. 2003-07-10. Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model. https://doi.org/10.1007/s002200000292

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