On the spectral analysis of second-order Markov chains
Persi Diaconis, Laurent Miclo (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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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...