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

2009/03/17 by Montrieux, William Bordeaux, Sjoestrand, Johannes
#35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0903.2937

Abstract

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.

Related

• Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations
• Spectral properties of non-self-adjoint operators
• Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators
• Weyl Law on Asymptotically Euclidean Manifolds
• Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations