Some Abstract Wegner Estimates with Applications

Mostafa Sabri

doi:10.1007/s11005-013-0666-x

Some Abstract Wegner Estimates with Applications

Mostafa Sabri

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Abstract

We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum graphs with random edge length or random vertex coupling. We allow the coupling constants describing the randomness to be correlated and to have quite general distributions.

Original language	English (US)
Pages (from-to)	311-339
Number of pages	29
Journal	Letters in Mathematical Physics
Volume	104
Issue number	3
DOIs	https://doi.org/10.1007/s11005-013-0666-x
State	Published - Mar 2014

Keywords

quantum graphs
random operators
sparse potentials
Wegner estimates

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-013-0666-x

Cite this

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abstract = "We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum graphs with random edge length or random vertex coupling. We allow the coupling constants describing the randomness to be correlated and to have quite general distributions.",

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author = "Mostafa Sabri",

year = "2014",

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doi = "10.1007/s11005-013-0666-x",

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AB - We prove some abstract Wegner bounds for random self-adjoint operators. Applications include elementary proofs of Wegner estimates for discrete and continuous Anderson Hamiltonians with possibly sparse potentials, as well as Wegner bounds for quantum graphs with random edge length or random vertex coupling. We allow the coupling constants describing the randomness to be correlated and to have quite general distributions.

KW - quantum graphs

KW - random operators

KW - sparse potentials

KW - Wegner estimates

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JF - Letters in Mathematical Physics

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Some Abstract Wegner Estimates with Applications

Abstract

Keywords

ASJC Scopus subject areas

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