Large deviation results for Multitype Galton-Watson trees

Details Large deviation results for Multitype Galton-Watson trees Large deviation results for Multitype Galton-Watson trees

2010-09-15

arxiv.org/abs/1009.3036v3

Mathematics

Probability

20 pages. arXiv admin note: substantial text overlap with arXiv:math/0306045 by other authors

Scientific paper

Using the notion of consistency of empirical measures, under fairly general assumption we prove a joint large deviation principles in $n$ for the empirical pair measure and empirical offspring measure of multitype Galton-Watson tree conditioned to have exactly $n$ vertices in the weak topology. From these results we obtain large deviation principle for empirical pair measure of Markov chains indexed by simply generated trees obtain by conditioning Galton-Watson trees on the total number of vertices. For the case where the offspring law of the tree is geometric distribution with parameter $\sfrac{1}{2}$, we get an exact rate function. All our rate functions are expressed in terms of relative entropies.

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