Average error for spectral asymptotics on surfaces

Spectral Asymptotics of Laplace Operators on Surfaces with Cusps

Asymptotics for sliced average variance estimation

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve √ n consistency even when each slice contains only two data points. However, SAVE cannot be √ n consistent and it even turns...

Spectral asymptotics for canonical systems

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl–Titchmarsh and spectral functions of 2×2 first order canonical systems. Our results improve several classical results and solve open problems posed by previous authors. Furthermore, they are applied to radial Dirac and radial Schrödinger operators as well as to Kr...

Irregular Spectral Asymptotics

Spectral Statistics on Zoll Surfaces

The subject of this article is a family of (partly conjectural) spectral invariants of a Laplace operator with a discrete spectrum 2j known as its k-level correlation functions Pk and level spacings distribution v. The 2-level (or pair) correlation function P2, for instance, measures the asymptotic number of spacings 2* 2* between normalized eigenvalues 2* as the eigenvalues tend to infinity. T...