arXiv subjects

William Bordeaux Montrieux

Publications and source records attributed to William Bordeaux Montrieux.

3 recordsLinked to original sources

arXiv2013

Estimation de résolvante et construction de quasimode près du bord du pseudospectre

We consider a non-self-adjoint pseudodifferential operator in the semi-classical limit $(h\to 0)$. The principal symbol is given by p. We know that the resolvent $(z-P)^{-1}$ exists inside the range up to a distance $O((h\ln\frac{1}{h})^{\frac{k}{k+1}})$ from certain boundary points, where $k\in\{2,4,...\}$. In this work, we improve the resolvent estimates given by different authors in the case k=2 and in dimension one. For the proof, we will construct quasimodes by a scaling for z very close to the boundary. We give some applications of this formula.

math.SP↗

arXiv2011

Loi de Weyl presque sure pour un systeme differentiel en dimension 1

We consider quite general differential operators on the circle with a small random lower order perturbation. We embrace two points a view, the semiclassical and the high energy limits. We show (a) in the semiclassical limit, that the eigenvalues inside a subdomain of the pseudospectrum are distributed according to a Weyl law with a probability close to 1, (b) that the large eigenvalues obey a Weyl law almost surely.

math.SP↗

arXiv2009

Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds

In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.

math.SP↗