Deformed matrix models: Growth Rates and KPZ Lower Tail Asymptotics

by Dr Carla Mariana Da Silva Pinheiro (USP)

Thursday 2 Apr 2026, 14:00 → 15:00 Europe/Brussels

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

This study investigates the multiplicative statistics of unitary random matrix ensembles subjected to a parameter-dependent deformation of the underlying probability measure. While previous literature characterized these deformations in the context of bounded or decaying parameters, the regime of growing parameters remained open. In this work, we bridge this gap by extending existing results to accommodate a parameter that grows at a controlled rate relative to the matrix size N.
In particular, we establish that under appropriate scaling, the underlying multiplicative statistics of the matrix model converge to the ones of the lower tail of the Kardar-Parisi-Zhang (KPZ) equation. This connection provides a new perspective on the universality of the KPZ fluctuations within the framework of deformed unitary ensembles. The seminar is based on the pre-print ArXiV: 2511.01120.