The Role of Kemeny's Constant in Properties of Markov Chains
Manage episode 151501848 series 1029398
Contenu fourni par Hamilton Institute. Tout le contenu du podcast, y compris les épisodes, les graphiques et les descriptions de podcast, est téléchargé et fourni directement par Hamilton Institute ou son partenaire de plateforme de podcast. Si vous pensez que quelqu'un utilise votre œuvre protégée sans votre autorisation, vous pouvez suivre le processus décrit ici https://fr.player.fm/legal.
Speaker: Prof. J. J. Hunter Abstract: In a finite m-state irreducible Markov chain with stationary probabilities {\pi_i} and mean first passage times m_{ij} (mean recurrence time when i=j) it was first shown, by Kemeny and Snell, that \sum_{j=1}^{m}\pi_jm_{ij} is a constant, K, not depending on i. This constant has since become known as Kemeny’s constant. We consider a variety of techniques for finding expressions for K, derive some bounds for K, and explore various applications and interpretations of theseresults. Interpretations include the expected number of links that a surfer on the World Wide Web located on a random page needs to follow before reaching a desired location, as well as the expected time to mixing in a Markov chain. Various applications have been considered including some perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.
…
continue reading
63 episodes