Precise large deviation calculations in statistical field theories with weak noise

Timo Schorlepp^1*

¹Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

* Presenter:Timo Schorlepp, email:timo.schorlepp@nyu.edu

Large deviation theory provides a common theoretical framework to compute probabilities of rare events in stochastic systems out of equilibrium. The theory consists of a saddlepoint evaluation of the path integral that describes the stochastic process under study, and has successfully been used in various physical systems such as interface growth, active matter, lattice gases/macroscopic fluctuation theory, fluid turbulence, and so forth. In this talk, I will describe recent progress in going beyond leading-order large deviation asymptotics, and hence developing tractable and general methods to evaluate 1-loop or Gaussian corrections around nontrivial large deviation minimizers. I will focus on Langevin equations and statistical field theories subject to weak noise here, discuss some technical aspects and surprises, and show applications to Burgers and Navier-Stokes turbulence. The presentation is based on and extends [Schorlepp, Grafke, Grauer. J. Stat. Phys. 2023 190(3):50] and [Schorlepp, Tong, Grafke, Stadler. Stat. Comput. 2023 33(6):137].

Keywords: non-equilibrium statistical mechanics, large deviation theory, Fredholm determinants, matrix Riccati equations, fluid turbulence