4 citations · 6 across the 13 of their papers we have counts for
18 papers
Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature
Alix Deleporte, Jean Lagacé, Marc Rouveyrol
Given a Riemannian manifold endowed with a smooth metric satisfying upper and lower sectional curvature bounds, we show an equivalence property between the n…
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…
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…
Spectral estimates on hyperbolic surfaces and a necessary condition for observability of the heat semigroup on manifolds
Alix Deleporte, Marc Rouveyrol
This article is a continuation of arXiv:2401.14977. We study the concentration properties of spectral projectors on manifolds, in connection with the uncertainty principle. In arXi…
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…
Real-analytic geodesics in the Mabuchi space of Kähler metrics and quantization
Alix Deleporte, Steve Zelditch
We prove the convergence of quantized Bergman geodesics to the Mabuchi geodesics for the initial value problem, in the case of real-analytic initial data and in short time. This pa…
Universality for free fermions and the local Weyl law for semiclassical Schrödinger operators
Alix Deleporte, Gaultier Lambert
We study local asymptotics for the spectral projector associated to a Schrödinger operator on in the semiclassical limit as . We prove local…
A direct approach to the analytic Bergman projection
Alix Deleporte, Michael Hitrik, Johannes Sjoestrand
We develop a direct approach to the semiclassical asymptotics for Bergman projections in exponentially weighted spaces of holomorphic functions, with real analytic strictly plurisu…
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…
WKB eigenmode construction for analytic Toeplitz operators
Alix Deleporte
We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These almost eigenfunctions follow the WKB ansatz; the er…
The Bergman kernel in constant curvature
Alix Deleporte
We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect t…
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…
Quantum selection for spin systems
Alix Deleporte
We report mathematical results on the process by which quantum order by disorder takes place for spin systems. The selection rules follow the influence of several competing contrib…
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…