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math.PR2025
Fluctuations of two-dimensional determinantal processes associated with Berezin--Toeplitz operators
Alix Deleporte, Gaultier Lambert
We consider a new class of determinantal point processes in the complex plane coming from the ground state of free fermions associated with Berezin--Toeplitz operators. These proce…
math.PR2025
Bulk asymptotics of the Gaussian -ensemble characteristic polynomial
Gaultier Lambert, Elliot Paquette
The Gaussian -ensemble (GE) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomia…
math.PR2024
Subcritical multiplicative chaos and the characteristic polynomial of the CE
Gaultier Lambert, Joseph Najnudel
The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular beta-ensembles.…