4 citations · 6 across the 13 of their papers we have counts for
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Regular Bohr-Sommerfeld rules for non-self-adjoint Berezin--Toeplitz operators and complex Lagrangian states
Alix Deleporte, Yohann Le Floch
We describe the eigenvalues and eigenvectors of real-analytic, non-self-adjoint Berezin--Toeplitz operators, up to exponentially small error, on complex one-dimensional compact man…
Widom's conjecture: variance asymptotics and entropy bounds for counting statistics of free fermions
Alix Deleporte, Gaultier Lambert
We obtain a central limit theorem for bulk counting statistics of free fermions in smooth domains of with an explicit description of the covariance structure. This a…
The Szegő kernel in analytic regularity and analytic Fourier Integral Operators
Alix Deleporte
We build a general theory of microlocal (homogeneous) Fourier Integral Operators in real-analytic regularity, following the general construction in the smooth case by Hörmander and…
Central limit theorem for smooth statistics of one-dimensional free fermions
Alix Deleporte, Gaultier Lambert
We consider the determinantal point processes associated with the spectral projectors of a Schrödinger operator on , with a smooth confining potential. In the semiclass…
Uniform spectral asymptotics for semiclassical wells on phase space loops
Alix Deleporte, San Vũ Ng\d{o}c
We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum on a closed curve. We derive…
Fractional exponential decay in the forbidden region for Toeplitz operators
Alix Deleporte
We prove several results of concentration for eigenfunctions in Toeplitz quantization. With mild assumptions on the regularity, we prove that eigenfunctions are awa…
Toeplitz operators with analytic symbols
Alix Deleporte
We provide asymptotic formulas for the Bergman projector and Berezin-Toeplitz operators on a compact K{ä}hler manifold. These objects depend on an integer N and we study, in the li…
Low-energy spectrum of Toeplitz operators with a miniwell
Alix Deleporte
In the semiclassical limit, it is well-known that the first eigenvector of a Toeplitz operator concentrates on the minimal set of the symbol. In this paper, we give a more precise…
Low-energy spectrum of Toeplitz operators: the case of wells
Alix Deleporte
In the 1980s, Helffer and Sjöstrand examined in a series of articles the concentration of the ground state of a Schrödinger operator in the semiclassical limit. In a similar spirit…