Entropy equipartition along almost geodesics in negatively curved groups

The classical Shannon-McMillan-Breiman (SMB) theorem states that for an ergodic measure preserving transformation on a probability space, the rate of uncertainty measured by mathematical entropy can be observed in almost every orbit of the system.

We explain how to use an abstract skew product construction in order to prove such results for measure preserving actions of negatively curved groups, with refinements being taken along random almost geodesics. Joint work with Amos Nevo.