Scaling limits of the Gaussian beta-ensemble characteristic polynomial (Gaultier Lambert, KTH)

11.06.2024 16:15 – 18:15

The Gaussian beta-ensemble or one-dimensional log-gas is a classical model of random matrix theory which describes a gas of electric charges confined on the real line which interact via the two-dimensional Coulomb kernel. I will report on recent asymptotic results for the characteristic polynomial of these ensembles at general inverse-temperature beta. These asymptotics involve the so-called Sine and Airy processes, as well as a Gaussian log-correlated field, and they should be compared to the classical Plancherel-Rotach asymptotics for the Hermite polynomials (β = ∞). The proof are based on the Dumitriu-Edelman tridiagonal representation of the Gaussian beta-ensemble and the transfer matrix method. If time permits, I will also mention some connections to Gaussian multiplicative chaos. Joint work with Elliot Paquette (McGill University)

(note the unusual time)

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre