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On the spectral analysis of second-order Markov chains

Abstract : Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm that the resort to second order Markov chains is an interesting option to improve the speed of convergence to equilibrium.
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https://hal.archives-ouvertes.fr/hal-00719047
Contributor : Laurent Miclo Connect in order to contact the contributor
Submitted on : Wednesday, July 18, 2012 - 7:33:16 PM
Last modification on : Friday, December 24, 2021 - 3:18:04 PM
Long-term archiving on: : Friday, October 19, 2012 - 3:07:02 AM

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  • HAL Id : hal-00719047, version 1

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Persi Diaconis, Laurent Miclo. On the spectral analysis of second-order Markov chains. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2013, 22 (3), pp.573-621. ⟨hal-00719047⟩

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