Regular Markov chains for which the transition matrix has large exponent Original Research Article

In this paper we analyze properties of transition matrices image of regular Markov chains whose exponent (index of primitivity) is bounded below by left floor((n−1)2+1)/2right floor+2. Our investigation leads to a proof that for such a T, the corresponding condition number image, where Q=I−T. We go on to show that if image is a perturbation of T such that T+E is also a transition matrix for a regular Markov chain and π and image are the stationary distribution vectors of T and T+E, respectively, then image and image. Many of the techniques used to establish these results are combinatorial in nature.