The Geometry Of Markov Chain Limit Theorems
Markov Processes And Related Fields
Mathematics and Computer Science
In this paper, we use a geometric viewpoint to prove several of the fundamental theorems on the convergence of Markov chains. In particular, we determine the long-term behavior of Markov chains geometrically both when they are irreducible and aperiodic and when they are not. By viewing the transition matrix of a Markov chain as a linear transformation from the standard simplex to itself, we simplify the traditional, matrix-based descriptions and proofs of the long-term behavior of Markov chains.
Bernhard, James. 2013. "The Geometry of Markov Chain Limit Theorems." Markov Processes And Related Fields 19(1): 99-124.