A large-deviation theorem for tree-indexed Markov chains
| dc.creator | Dembo, Amir | |
| dc.creator | Morters, Peter | |
| dc.creator | Sheffield, Scott | |
| dc.date | 2003-06-02 | |
| dc.date.accessioned | 2026-07-07T04:58:31Z | |
| dc.date.available | 2026-07-07T04:58:31Z | |
| dc.description | Given a finite typed rooted tree $T$ with $n$ vertices, the {\em empirical subtree measure} is the uniform measure on the $n$ typed subtrees of $T$ formed by taking all descendants of a single vertex. We prove a large deviation principle in $n$, with explicit rate function, for the empirical subtree measures of multitype Galton-Watson trees conditioned to have exactly $n$ vertices. In the process, we extend the notions of shift-invariance and specific relative entropy--as typically understood for Markov fields on deterministic graphs such as $\mathbb Z^d$--to Markov fields on random trees. We also develop single-generation empirical measure large deviation principles for a more general class of random trees including trees sampled uniformly from the set of all trees with $n$ vertices. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306045 | |
| dc.identifier | http://arxiv.org/abs/math/0306045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67667 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60G20; 80B20; 37A50 | |
| dc.title | A large-deviation theorem for tree-indexed Markov chains | |
| dc.type | text |