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