Directed Forests and the Constancy of Kemeny's Constant
| dc.contributor.author | Kirkland, Steve | |
| dc.date.accessioned | 2023-02-21T20:03:15Z | |
| dc.date.available | 2023-02-21T20:03:15Z | |
| dc.date.issued | 2019-11-02 | |
| dc.date.submitted | 2023-02-21T19:12:37Z | en_US |
| dc.description.abstract | Consider a discrete-time, time-homogeneous Markov chain on states 1, ... , n whose transition matrix is irreducible. A result of Kemeny reveals that the expected number of steps needed to arrive at a randomly chosen destination state starting from state j is (surprisingly) independent of the initial state j. In this note, we consider Kemeny's result from the perspective of algebraic combinatorics, and provide an intuitive explanation for its independence on the initial state j. The all minors matrix tree theorem is the key tool employed. | en_US |
| dc.identifier.doi | 10.1007/s10801-019-00919-1 | |
| dc.identifier.uri | http://hdl.handle.net/1993/37176 | |
| dc.language.iso | eng | en_US |
| dc.publisher | Springer Nature | en_US |
| dc.rights | open access | en_US |
| dc.subject | Markov chain | en_US |
| dc.subject | Kemeny's constant | en_US |
| dc.subject | All minors matrix tree theorem | en_US |
| dc.title | Directed Forests and the Constancy of Kemeny's Constant | en_US |
| dc.type | research article | en_US |
| local.author.affiliation | Faculty of Science::Department of Mathematics | en_US |
| oaire.citation.endPage | 84 | en_US |
| oaire.citation.startPage | 81 | en_US |
| oaire.citation.title | Journal of Algebraic Combinatorics | en_US |
| oaire.citation.volume | 53 | en_US |
| project.funder.identifier | https://doi.org/10.13039/501100000038 | en_US |
| project.funder.name | Natural Sciences and Engineering Research Council of Canada | en_US |