Conditional Phenomena in Time and Space

Random phenomena are ubiquitous throughout science and engineering. Beyond the study of stochastic models in their own right, it is of importance in many applications to understand what information can be extracted on the basis of observed data. Mathematically, such “data assimilation” problems motivate the investigation of probabilistic phenomena that arise from conditioning. This topic has connections to several areas of probability, ergodic theory, measure theory, and statistical mechanics, as well as practical implications for the design and analysis of algorithms for data assimilation in complex systems. In this talk I will give an overview of some old and new problems in this setting, with emphasis on the behavior of conditional distributions and their approximations on long time intervals and in high dimension