  Stochastic models of evolution (Markov random fields on trivalent trees)
generally assume that different characters (different runs of the stochastic
process) are independent and identically distributed. In this paper we take the
first steps towards addressing dependent characters. Specifically we show that,
under certain technical assumptions regarding the evolution of individual
characters, we can detect any significant, history independent, correlation
between any pair of multistate characters. For the special case of the
Cavender-Farris-Neyman (CFN) model on two states with symmetric transition
matrices, our analysis needs milder assumptions. To perform the analysis, we
need to prove a new concentration result for multistate random variables of a
Markov random field on arbitrary trivalent trees: we show that the random
variable counting the number of leaves in any particular subset of states has
variance that is subquadratic in the number of leaves.
