Universality for free fermions point processes

Abstract: I report on recent results obtained with A. Deleporte on universality of local statistics for the ground state of a free Fermi gas confined in a generic potential on ℝ^n. This model was introduced by Macchi in 1975 and it forms a determinantal point process whose kernel is the spectral projector associated to a Schrödinger operator −ℏ^2Δ+V. I will explain how to obtain the asymptotics of the kernel of this projector as ℏ→0 using methods from semiclassical analysis and discuss some probabilistic consequences. In particular, this implies universality of microscopic fluctuations, both in the bulk and around regular boundary points.

mathematical physics

Audience: researchers in the discipline

( video )

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