A large-deviation theorem for tree-indexed Markov chains

Details A large-deviation theorem for tree-indexed Markov chains A large-deviation theorem for tree-indexed Markov chains

2003-06-02

arxiv.org/abs/math/0306045v1

Mathematics

Probability

23 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A large-deviation theorem for tree-indexed Markov chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A large-deviation theorem for tree-indexed Markov chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A large-deviation theorem for tree-indexed Markov chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484892