The Role of Kemeny's Constant in Properties of Markov Chains
By Jeffrey J. Hunter. 2012
85 citations recorded by the source corpus.
In a finite irreducible Markov chain with stationary probabilities {π i } and mean first passage times m ij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell (1960), that is a constant, K, (Kemeny's constant) not depending on i. A variety of techniques for finding expressions and bounds for K are given. The main interpretation focuses on its role as the expected time to mixing in a Markov chain. Various applications are considered including perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7f2bec4b051578f68757232071c337ab517c0f67
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Statistics and Probability
Citations in the corpus
- Algebraic aspects of the normalized Laplacian (2016, background): “Given a graph G, Kemeny’s constant, denoted K(G), is the expected first passage time from an unknown starting point in the graph to an unknown destination point in the graph (see [17] for more information).”