The landscape law for the integrated density of states

G. David; M. Filoche; S. Mayboroda

doi:10.1016/j.aim.2021.107946

The landscape law for the integrated density of states

G. David, M. Filoche, S. Mayboroda

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator L=−Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.

Original language	English (US)
Article number	107946
Journal	Advances in Mathematics
Volume	390
DOIs	https://doi.org/10.1016/j.aim.2021.107946
State	Published - Oct 29 2021

Bibliographical note

Funding Information:
David is supported in part by the H2020 grant GHAIA 777822, and Simons Foundation grant 601941, GD. Filoche is supported in part by Simons Foundation grant 601944, MF. Mayboroda is supported in part by the NSF grants DMS 1344235, DMS 1839077, and Simons Foundation grant 563916, SM.

Publisher Copyright:
© 2021

Keywords

Integrated density of states
Landscape
Localization
Weyl law

Access

10.1016/j.aim.2021.107946

OpenUrl availability

Full text

Cite this

@article{ea0a8d46d9be4cc59bd79726277a9690,

title = "The landscape law for the integrated density of states",

abstract = "The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schr{\"o}dinger operator L=−Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.",

keywords = "Integrated density of states, Landscape, Localization, Weyl law",

author = "G. David and M. Filoche and S. Mayboroda",

note = "Funding Information: David is supported in part by the H2020 grant GHAIA 777822, and Simons Foundation grant 601941, GD. Filoche is supported in part by Simons Foundation grant 601944, MF. Mayboroda is supported in part by the NSF grants DMS 1344235, DMS 1839077, and Simons Foundation grant 563916, SM. Publisher Copyright: {\textcopyright} 2021",

year = "2021",

month = oct,

day = "29",

doi = "10.1016/j.aim.2021.107946",

language = "English (US)",

volume = "390",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - The landscape law for the integrated density of states

AU - David, G.

AU - Filoche, M.

AU - Mayboroda, S.

N1 - Funding Information: David is supported in part by the H2020 grant GHAIA 777822, and Simons Foundation grant 601941, GD. Filoche is supported in part by Simons Foundation grant 601944, MF. Mayboroda is supported in part by the NSF grants DMS 1344235, DMS 1839077, and Simons Foundation grant 563916, SM. Publisher Copyright: © 2021

PY - 2021/10/29

Y1 - 2021/10/29

N2 - The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator L=−Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.

AB - The present paper establishes non-asymptotic estimates from above and below on the integrated density of states of the Schrödinger operator L=−Δ+V, using a counting function for the minima of the localization landscape, a solution to the equation Lu=1.

KW - Integrated density of states

KW - Landscape

KW - Localization

KW - Weyl law

UR - http://www.scopus.com/inward/record.url?scp=85111804526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85111804526&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2021.107946

DO - 10.1016/j.aim.2021.107946

M3 - Article

AN - SCOPUS:85111804526

SN - 0001-8708

VL - 390

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107946

ER -

The landscape law for the integrated density of states

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this