Large deviation results for critical multitype galton-watson trees

In this paper, we prove a joint large deviation principle in n for the empirical pair measure and empirical offspring measure of critical multitype Galton-Watson trees conditioned to have exactly n vertices in the weak topology. From this result we extend the large deviation principle for the empirical pair measures of Markov chains on simply generated trees to cover offspring laws which are not treated by [10, Theorem 2.1]. For the case where the offspring law of the tree is a geometric distribution with parameter (Formula presented) we get an exact rate function. All our rate functions are expressed in terms of relative entropies.