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Log-Concavity and the Spectral Gap of Stochastic Matrices

Published online by Cambridge University Press:  01 September 1997

EKKEHARD WEINECK
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, 33501 Bielefeld, Germany

Abstract

Let Q be a stochastic matrix and I be the identity matrix. We show by a direct combinatorial approach that the coefficients of the characteristic polynomial of the matrix IQ are log-concave. We use this fact to prove a new bound for the second-largest eigenvalue of Q.

Type
Research Article
Copyright
1997 Cambridge University Press

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