Interlacing eigenvalues in time reversible Markov chains (Q2757613)

For irreducible, reversible, finite state Markov chains the author observes that two sets of eigenvalues related to the transition rate matrix \(Q\), \((\lambda_0,\dots,\lambda_m)\) and \((\nu_1,\dots,\nu_m)\), are interlaced so that \(\lambda_0<\nu_1<\lambda_1<\cdots< \gamma_m< \lambda_m\). Many quantities associated with \({\mathcal L}_\pi T_A\), the distribution of the first time to \(A\) starting in steady state, can be expressed in terms of these eigenvalues, and the interlacing property can be exploited to obtain approximations.