Ramon van Handel (Princeton University)
Title: Conditional Ergodicity
Abstract:
What probabilistic phenomena can arise when a random system is
conditioned on partial information? Such questions are of fundamental
interest to the understanding of conditional distributions, and at the same
time have implications for applications ranging from GPS navigation to
weather forecasting. A general understanding of classical problems of this
kind, dating back at least to Blackwell (1957), has only recently been
obtained. At the same time, new questions and phenomena that arise in
high-dimensional problems, such as conditional phase transitions and decay
of correlations, are only beginning to be addressed. I will give an
overview of some old and new problems in this area, with emphasis on the
behavior of conditional distributions in high dimension and connections with
statistical mechanics and multidimensional ergodic theory.