Path-wise large deviations theory and some of its applications

I gave the following talk at the Hunter College Mathematics Colloquium. Many thanks to Vincent R Martinez for inviting me.

Abstract:

Since the work of Ellis in the eighties, we have known that large deviations theory gives us a natural way of making the sorts of asymptotic statements about probability which are often found in equilibrium statistical physics. Today large deviations theory remains a promising technique with which to answer questions in more complicated areas, like non-equilibrium statistical physics and statistical learning. In this talk I will discuss my outlook on this topic and some interesting domains of application. I will first review what a ‘large deviations principle’ is and why one might ever be interested in large deviations theory. I will go on to discuss a particular large deviations principle called the Freidlin–Wentzell theorem, and show how it secretly underlies a recent approach to statistical physics called stochastic thermodynamics. I will conclude with a brief discussion of how this story changes when the trajectory of a random process is coupled to some other process, and what sorts of questions that allows us to consider in physics and machine learning.

Details: link to website