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Multiplicatively closed Markov models must form Lie algebras
Citation
Sumner, JG, Multiplicatively closed Markov models must form Lie algebras, ANZIAM Journal, 59, (2) pp. 240-246. ISSN 1446-1811 (2017) [Refereed Article]
Copyright Statement
Copyright 2017 Australian Mathematical Society
DOI: doi:10.1017/S1446181117000359
Abstract
We prove that the probability substitution matrices obtained from a continuous-time Markov chain form a multiplicatively closed set if and only if the rate matrices associated with the chain form a linear space spanning a Lie algebra. The key original contribution we make is to overcome an obstruction, due to the presence of inequalities that are unavoidable in the probabilistic application, which prevents free manipulation of terms in the Baker–Campbell–Haursdorff formula.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | multiplicative closure, Markov models, semigroups, phylogenetics, lie algebras, continuous-time Markov chains |
| Research Division: | Mathematical Sciences |
| Research Group: | Applied mathematics |
| Research Field: | Biological mathematics |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding knowledge |
| Objective Field: | Expanding knowledge in the mathematical sciences |
| UTAS Author: | Sumner, JG (Associate Professor Jeremy Sumner) |
| ID Code: | 122652 |
| Year Published: | 2017 |
| Funding Support: | Australian Research Council (DP150100088) |
| Web of Science® Times Cited: | 7 |
| Deposited By: | Mathematics and Physics |
| Deposited On: | 2017-11-21 |
| Last Modified: | 2022-07-04 |
| Downloads: | 0 |
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