The delocalized phase of the Anderson Hamiltonian in 1-D

DOI10.1214/22-aop1591arXiv2102.05393MaRDI QIDQ6045511

Cyril Labbé, Laure Dumaz

Publication date: 31 May 2023

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.05393

zbMATH Keywords

diffusioncanonical systemsDirac operatordelocalizationAnderson Hamiltonianstrong resolvent convergenceHill's operator

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random operators and equations (aspects of stochastic analysis) (60H25) Diffusion processes (60J60)

Related Items (3)

Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in \(d\le 3\) ⋮ Anderson localization for the 1-d Schrödinger operator with white noise potential ⋮ Localization crossover for the continuous Anderson Hamiltonian in 1-d

Cites Work

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• The scaling limit of the critical one-dimensional random Schrödinger operator
• Spectral theory of ordinary differential operators
• Eigenvectors of the 1-dimensional critical random Schrödinger operator
• Schrödinger operators and de Branges spaces.
• The random matrix hard edge: rare events and a transition
• Localization of the continuous Anderson Hamiltonian in 1-d
• The \(\mathrm{Sine}_{\beta}\) operator
• From sine kernel to Poisson statistics
• From random matrices to stochastic operators
• [https://portal.mardi4nfdi.de/wiki/Publication:4134658 On spectra of the Schr�dinger operator with a white Gaussian noise potential]
• Random Schrödinger operators on long boxes, noise explosion and the GOE

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