Digraph-based conditioning for Markov chains (Q1827500)

For an irreducible stochastic matrix \(T\), the author considers a certain condition number \(c(T)\), which measures the stability of the corresponding stationary distribution when \(T\) is perturbed, and then characterizes the strongly connected directed graphs \(D\) such that \(c(T)\) is bounded as \(T\) ranges over \(\mathcal S_D\), the set of stochastic matrices whose directed graph is contained in \(D\). For those digraphs \(D\) for which \(c(T)\) is bounded, the maximum value of \(\{c(T)\mid T\) ranges over \(\mathcal S_D\}\) is determined.