43 citations · 74 across the 21 of their papers we have counts for
28 papers
Approximating sub-riemannian structures by Riemannian metrics and spectral convergence
Leo Harakeh, Luc Hillairet
We construct an approximating sequence of Riemannian metrics tailored to a given sub-Riemannian structure. We prove that the sequence of associated Riemannian volumes converge to P…
Cauchy Data for 1D singular Schrödinger operators
Luc Hillairet, Jeremy L. Marzuola
We study semiclassical 1-D Schrödinger operators of the form on a finite interval for . We show tha…
Generic simplicity of ellipses
Luc Hillairet, Chris M. Judge
We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the…
Spectral asymptotics for sub-Riemannian Laplacians
Yves Colin de Verdìère, Luc Hillairet, Emmanuel Trélat
We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic operators. The main objective is to obtain quantum ergodicity results, what we have achieved in th…
Eigenvalue spacing for 1D singular Schrödinger operators
Luc Hillairet, Jeremy L. Marzuola
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schrödinger operators with singular potentials on the half-line.…
Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent
Luc Hillairet, Helen Jenne, Kilian Raschel
In the field of enumeration of walks in cones, it is known how to compute asymptotically the number of excursions (finite paths in the cone with fixed length, starting and ending p…