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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1007/978-3-642-23348-7_12

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1869-1862

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Estimates on the amplitude of the first Dirichlet

Authors: Persi Diaconis Laurent Miclo
Publish Date: 2015/10/29
Volume: 59, Issue: 2, Pages: 205-226
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Abstract

Consider a finite absorbing Markov generator irreducible on the nonabsorbing states PerronFrobenius theory ensures the existence of a corresponding positive eigenvector ϕ The goal of the paper is to give bounds on the amplitude max ϕ/min ϕ 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 quasistationarity to the convergence to equilibrium of related ergodic processes as seen by Diaconis and Miclo 2014

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