We are pleased to announce that Dr. Timo Schorlepp, Courant Instructor and Assistant Professor at New York University, has received the Department Dissertation Award. In his dissertation, he explored how instantons and fluctuations can be used to predict rare events in complex systems.
Predicting the probabilities and typical shapes of rare but impactful events—such as high waves and strong vortices in fluid flows, or extreme climate events—is a major challenge across
many scientific and engineering disciplines. Large deviation theory provides a principled framework for addressing these problems in stochastic systems. Here, the probabilities of extreme events are
approximated by focusing on the most probable path—the “instanton”—that leads to a prescribed outcome. My doctoral thesis focused, among other things, on: (i) robust
instanton calculations via optimal control techniques, and (ii) more precise probability estimates by exactly calculating Gaussian fluctuations around the instanton, using Riccati
equations and Fredholm determinants. These methods will be illustrated through examples of extreme events in fluid turbulence (Burgers and Navier-Stokes equations) and nonlinear-
interface growth (Kardar-Parisi-Zhang equation). The overarching goal of this work is to provide more robust and precise predictions for rare phenomena in complex systems.
Abstract by Dr. Schorlepp.