A large-deviation theorem for tree-indexed Markov chains

arXivmath/0306045MaRDI QIDQ6472889

Amir Dembo, Scott Sheffield, Peter Mörters

Publication date: 2 June 2003

Abstract: 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.

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Dynamical systems and their relations with probability theory and stochastic processes (37A50)

This page was built for publication: A large-deviation theorem for tree-indexed Markov chains

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6472889)