Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks
Résumé
Consider a finite absorbing Markov generator, irreducible on the non-absorbing states.
Perron-Frobenius theory ensures the existence of a corresponding positive eigenvector $\varphi$.
The goal of the paper is to give bounds on the amplitude $\max \varphi/\min\varphi$.
Two approaches are proposed: one using a path method and the other one, restricted to the reversible situation,
based on spectral estimates. The latter approach is extended to denumerable birth and death processes absorbing at 0 for
which infinity is an entrance boundary.
The interest of estimating the ratio is the reduction of the quantitative study of convergence
to quasi-stationarity to the convergence to equilibrium of related ergodic processes, as seen in [7].
Origine : Fichiers produits par l'(les) auteur(s)
Loading...