A well-known result in the theory of Markov chains, the Convergence Theorem, states that if we assume the chain to be aperiodic and irreducible, then its distribution converges to equilibrium. This thesis presents a selection of different methods aimed at tackling the problem of estimating how rapidly this happens. The techniques shown move from analytic, geometric or probabilistic considerations and each of them is followed by an example that illustrates the practical efficiency of the method.

A well-known result in the theory of Markov chains, the Convergence Theorem, states that if we assume the chain to be aperiodic and irreducible, then its distribution converges to equilibrium. This thesis presents a selection of different methods aimed at tackling the problem of estimating how rapidly this happens. The techniques shown move from analytic, geometric or probabilistic considerations and each of them is followed by an example that illustrates the practical efficiency of the method.

Mixing Times of Markov Chains: from Coupling to Paths

PIGNATELLI, FEDERICO MAURO
2023/2024

Abstract

A well-known result in the theory of Markov chains, the Convergence Theorem, states that if we assume the chain to be aperiodic and irreducible, then its distribution converges to equilibrium. This thesis presents a selection of different methods aimed at tackling the problem of estimating how rapidly this happens. The techniques shown move from analytic, geometric or probabilistic considerations and each of them is followed by an example that illustrates the practical efficiency of the method.
2023
Mixing Times of Markov Chains: from Coupling to Paths
A well-known result in the theory of Markov chains, the Convergence Theorem, states that if we assume the chain to be aperiodic and irreducible, then its distribution converges to equilibrium. This thesis presents a selection of different methods aimed at tackling the problem of estimating how rapidly this happens. The techniques shown move from analytic, geometric or probabilistic considerations and each of them is followed by an example that illustrates the practical efficiency of the method.
Markov Chains
Mixing Times
Stochastic Processes
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/71001