Timo Schorlepp (NYU)
Description
Salle 523, couloir 12-13, 5è étage
Precise large deviations in statistical field theories with weak noise
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 and the macroscopic fluctuation theory, fluid dynamics and turbulence, and so forth.
In this talk, I will describe recent progress in going beyond leading-order large deviation asymptotics, developing tractable and general methods to exactly evaluate 1-loop or Gaussian corrections around nontrivial large deviation minimizers for weak noise Langevin equations and field theories. To compute the corresponding large deviation prefactors, on the one hand, I will introduce an approach based on matrix Riccati differential equations, and on the other hand, I will show how alternatively formulating the prefactor in terms of Fredholm determinants or renormalized Carleman-Fredholm determinants and operator traces makes it feasible to evaluate these corrections in very high-dimensional systems.
To illustrate these points, I will show multiple examples of precise rare event estimates in statistical field theories, such as extreme growth events in the one-dimensional KPZ equation at short times, extreme concentrations of a randomly advected passive scalar, and extreme vortices and strain events in the stochastically forced incompressible Navier-Stokes equations.