Alix Deleporte Université Paris-Saclay
Semiclassical analysis of free fermions
Abstract:
To each orthogonal projector of finite rank N on
L2(ℝd) is associated
a point process on ℝd with N points, which gives the joint probability
density of fermions that fill the image of the projector.
The study of the statistical properties of these fermions, in the large
N limit, boils down to semiclassical spectral theory problems, some of
them well studied (the Weyl law gives a law of large numbers), some of
them new. In particular, the behaviour of the variance is linked with
the properties of commutators involving spectral projectors, which are
not so well understood.
In this talk, I will present my work in collaboration with Gaultier
Lambert (KTH) on this topic.