Title: Extremality of Markov models on trees, stochastic recursions, and entropy

The study of Markov models on trees evitably leads to considerations 
of stochastic recursions which have the flavour of renormalization 
group transformations. Convergence to a trivial fixed point then 
implies extremality of the corresponding measure which itself 
is equivalent to non-reconstructability, in information-theoretic language. 
How to deal with this recursion of infinite-dimensional objects
in a good way? We describe a method to show convergence 
to the trivial fixed point (possibly in non-trivial situations of a non-unique measure) 
which uses a suitable entropy function as a Lyapunov function. 


Joint work with M. Formentin