Spectral Theory for Weakly Reversible Markov Chains

-spectral gaps for time discrete reversible Markov chains

In this paper we study the spectral properties of Markov-operator on L -spaces. Lawler and Sokal (Trans. Amer. Math. Soc., 1988, 309, pp. 557-580) used isoperimetric constants for discrete and continuous time Markov chains to obtain a spectral gap at 1. For time discrete Markov chains this does not exclude periodic behavior. We define a new constant measuring the distance from periodicity and g...

G-PCCA: Spectral Clustering for Non-reversible Markov Chains

Spectral clustering methods are based on solving eigenvalue problems for the identification of clusters, e.g., the identification of metastable subsets of a Markov chain. Usually, real-valued eigenvectors are mandatory for this type of algorithms. The Perron Cluster Analysis (PCCA+) is a well-known spectral clustering method of Markov chains. It is applicable for reversible Markov chains, becau...

weak-reversible Markov chains

The theory of L-spectral gaps for reversible Markov chains has been studied by many authors. In this paper we consider positive recurrent general state space Markov chains with stationary transition probabilities. Replacing the assumption of reversibility by a less strong one, we still obtain a simple necessary and sufficient condition for the spectral gap property of the associated Markov oper...

Chapter 3 Reversible Markov Chains

Chapter 2 reviewed some aspects of the elementary theory of general nite irreducible Markov chains. In this chapter we specialize to reversible chains, treating the discrete and continuous-time cases in parallel. After section 3 we shall assume that we are dealing with reversible chains without continually repeating this assumption, and shall instead explicitly say \general" to mean not-necessa...

Some Inequalities for Reversible Markov Chains