Weak mixing of Markov measures on the boundary of free groups
Several recent methods for proving pointwise ergodic theorems for pmp actions of free groups critically use weak mixing properties of Markov measures on the boundary of a free group of finite rank. However, it was not known exactly which Markov measures are weak mixing. In joint work with Jenna Zomback, we give a complete characterization of such measures. It turns out that, under mild non-degeneracy assumptions, they are exactly the Markov measures arising from strictly irreducible
transition matrices – a condition introduced by Bufetov in 2000 for a different purpose. The proof of this characterization goes through proving equivalences with a new combinatorial condition on the action that we call chaining, which is interesting in its own right.