PIICQ September 2024: Fabio Deelan Cunden and Taro Kimura

lundi 30 sept. 2024, 16:00 → 18:00 Europe/Paris

Zoom

We will kick off the new academic year with two online talks by Fabio Deelan Cunden (Università degli Studi di Bari) and Taro Kimura (Université de Bourgogne) on September 30th.

Kimura.pdf

1 Random matrices, Young diagrams and plane trees

We consider ‘λ-shaped random matrices’, whose entries are i.i.d. in the boxes of a given Young diagram λ and zero elsewhere. In particular, we study their limiting spectral distribution when the shape λ is dilated by a growing factor N. The moments of such a distribution are a generalisation of Catalan numbers, and enumerate a combinatorial object which we call λ-plane trees: these are trees whose vertices are labelled in a way that is ‘compatible’ with λ. Based on joint works with Elia Bisi and Marilena Ligabò.

Orateur: Fabio Deelan Cunden (Università degli Studi di Bari)

2 Fredholm determinants from Schrödinger-type equations, and deformation of Tracy-Widom distribution

The Tracy-Widom distribution, defined via the Fredholm determinant associated with the Airy kernel, has emerged as a universal distribution in various contexts, including statistical mechanics, stochastic processes, and related fields. The aim of this presentation is to introduce our recent approach in establishing a novel deformation of the Tracy-Widom distribution, linked to a broad class of Schrödinger-type ODE systems. I will elucidate the underlying mathematical structures of this method, including a nonlinear integro-differential equation as a deformation of the Painlevé II equation, the hierarchical Poisson structure, and its connection to the isomonodromic system. This is based on a joint-work with Xavier Navand, https://arxiv.org/abs/2408.06888

Orateur: Taro Kimura (Université de Bourgogne)