The landscape law for the integrated density of states
Guy David, Marcel Filoche, and Svitlana Mayboroda
TL;DR
This paper introduces a method to estimate the integrated density of states for Schrödinger operators using the localization landscape, providing non-asymptotic bounds based on minima counting functions.
Contribution
It presents a novel approach linking the localization landscape to spectral estimates, offering explicit bounds for the integrated density of states.
Findings
Derived non-asymptotic upper and lower bounds
Connected landscape minima to spectral properties
Enhanced understanding of Schrödinger operator spectra
Abstract
The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schr\"odinger operator , using a counting function for the minima of the localization landscape, a solution to the equation .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.