Exposé de Joelle Ishak
Abstract:
Branching random walk is a stochastic process that combines the concepts of branching processes and random
walks, offering a powerful framework to study a wide range of phenomena, including population dynamics,
particle systems, and epidemic spreading.
Exposé Statistics of local level spacings in quantum chaology
Exposé de Peng Tian:
Abstract: We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal -- chaotic or regular -- dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards and many-body spectra of the Sachdev-Ye-Kitaev (SYK) Hamiltonians.
Exposé Topological expansion of unitary integrals and maps
Thomas Buc d'Alché's talk
Abstract: Consider integrals on the unitary group, with respect to the Haar measure. The asympotic expansion of such integrals when the dimension tends to infinity can be expressed in terms of maps, i.e. graphs embedded in surfaces. These particular maps generalize the monotone Hurwitz numbers.
Exposé Universality for least singular value of alpha-stable RM
Exposé de Michalis Louvaris
Abstract
This talk investigates the asymptotic behavior of the least singular value a heavy-tailed random matrix model, random matrices with alpha-stable entries. We establish that the asymptotic distribution is the same as in the models with finite variance, for example when the entries of the matrix are Gaussian random variables, as the dimension of the matrices grows to infinity.
The methods used to establish the result are based on the three step strategy, an important strategy developed in the last decade in the random matrix theory literature.