Parts | Days | Selection | Search | Updates | Downloads | Help
DY: Fachverband Dynamik und Statistische Physik
DY 15: Focus Session: Large Deviations and Rare Events II
DY 15.8: Talk
Monday, March 9, 2026, 17:15–17:30, ZEU/0114
Precise large deviations in statistical field theories with weak noise — •Timo Schorlepp1, Tobias Grafke2, Rainer Grauer3, Georg Stadler1, and Shanyin Tong4 — 1NYU Courant, USA — 2Warwick, UK — 3Bochum, Germany — 4UPenn, USA
Large deviation theory (LDT) 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 describing the stochastic process under study, and has successfully been used in various systems such as growing interfaces, active matter, lattice gases and macroscopic fluctuation theory, fluid dynamics and turbulence, etc. I will describe recent progress in going beyond leading-order LDT asymptotics, developing tractable methods to evaluate 1-loop (Gaussian) corrections around nontrivial LDT minimizers for weak noise Langevin equations and field theories. This allows for quantitative rare event probability estimates, beyond the usual log-asymptotics. To compute the corresponding LDT prefactors, I will present two complementary approaches based on either matrix Riccati differential equations, or (possibly renormalized) Fredholm determinants. I will illustrate these methods in multiple analytical/numerical examples: extreme growth events in the 1d KPZ equation at short times [1], extreme concentrations of a randomly advected passive scalar [2], and extreme strain events in the stochastically forced incompressible 3d Navier-Stokes equations [3]. References: [1] Schorlepp, Grafke, Grauer, J Stat Phys, 2023; [2] Schorlepp, Grafke, arXiv:2502.20114, 2025; [3] Schorlepp, Tong, Grafke, Stadler, Stat. Comput., 2023.
Keywords: large deviation theory; large deviation prefactor; operator determinant; Kardar-Parisi-Zhang equation; passive scalar