Moderate deviations for the stochastic six-vertex model and random matrices

by Guilherme Silva (Universidade de São Paulo)

Thursday 7 May 2026, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

The phenomenon of universality is central to random matrix theory and stochastic growth models. In one of its most celebrated forms, it establishes that the fluctuations of extremal eigenvalues in large Hermitian random matrices are described by the Tracy-Widom distribution, entirely irrespective of the original distribution of the matrix entries. Strikingly, across a broad family of 1+1-dimensional stochastic growth models - specifically those sharing the macroscopic symmetries of the Kardar-Parisi-Zhang equation - the long-time fluctuations of the growing interface are governed by this exact same Tracy-Widom distribution, linking the geometry of random growth to the spectrum of random matrices.

At the opposite end of the probability spectrum, large deviations in both stochastic growth and random matrices exhibit a very different behavior: they display universal scaling, but distinctly non-universal rate functions that depend on microscopic details.

A natural question then emerges: how do these systems transition from the universality of typical fluctuations to the non-universal regime of large deviations? In this talk, we will explore this crossover phenomenon, discussing recent moderate deviation results that (try to) bridge the gap between these two distinct regimes.