15 citations · 46 across the 7 of their papers we have counts for
10 papers
Poisson eigenvalue statistics for random Schrödinger operators on regular graphs
Leander Geisinger
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In…
A short proof of Weyl's law for fractional differential operators
Leander Geisinger
We study spectral asymptotics for a large class of differential operators on an open subset of with finite volume. This class includes the Dirichlet Laplacian, the fractiona…
Convergence of the density of states and delocalization of eigenvectors on random regular graphs
Leander Geisinger
Consider a random regular graph of fixed degree with vertices. We study spectral properties of the adjacency matrix and of random Schrödinger operators on such a graph as $…
The ground state energy of a polaron in a strong magnetic field
Rupert L. Frank, Leander Geisinger
We show that the ground state of a polaron in a homogeneous magnetic field and its energy are described by an effective one-dimensional minimization problem in the limit $B\to\…
Semi-classical analysis of the Laplace operator with Robin boundary conditions
Rupert L. Frank, Leander Geisinger
We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove…
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain
Rupert L. Frank, Leander Geisinger
Let -Δdenote the Dirichlet Laplace operator on a bounded open set in \mathbb{R}^d. We study the sum of the negative eigenvalues of the operator -h^2 Δ- 1 in the semiclassical limit…
Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator
Rupert L. Frank, Leander Geisinger
We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a t…
Sharp spectral estimates in domains of infinite volume
Leander Geisinger, Timo Weidl
We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - an…
Geometrical Versions of improved Berezin-Li-Yau Inequalities
Leander Geisinger, Ari Laptev, Timo Weidl
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in , . In particular, we derive upper bounds on Riesz means of order $σ…
Universal Bounds for Traces of the Dirichlet Laplace Operator
Leander Geisinger, Timo Weidl
We derive upper bounds for the trace of the heat kernel of the Dirichlet Laplace operator in an open set , . In domains of finite volume the result…