# Mathematics Colloquia and Seminars

In this talk we will discus the quantitative analysis concerning the asymptotic behavior of time inhomogeneous finite Markov chains. To study this behavior, we develop singular value techniques in the context of time inhomogeneous chains and introduce the notion of $c$-stability, which can be viewed as a generalization of the case when a time inhomogeneous chain admits an invariant measure. We describe some examples where these techniques yield quantitative results for time inhomogeneous chains.