Convergence of the density of states and delocalization of eigenvectors on random regular graphs

DOI10.4171/JST/114zbMath1384.60024arXiv1305.1039OpenAlexW2964104759MaRDI QIDQ906575

Leander Geisinger

Publication date: 22 January 2016

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.1039

zbMATH Keywords

random Schrödinger operatordensity of statesrandom regular graphdelocalization of eigenvectorslocal spectral distribution

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (14)

On quantum percolation in finite regular graphs ⋮ Quantitative equidistribution of eigenfunctions for toral Schrödinger operators ⋮ On the almost eigenvectors of random regular graphs ⋮ Local Kesten-McKay law for random regular graphs ⋮ Spectrum of random d‐regular graphs up to the edge ⋮ Quantum ergodicity for the Anderson model on regular graphs ⋮ Eigenvector delocalization for non‐Hermitian random matrices and applications ⋮ Structure of eigenvectors of random regular digraphs ⋮ Moments of the inverse participation ratio for the Laplacian on finite regular graphs ⋮ Poisson eigenvalue statistics for random Schrödinger operators on regular graphs ⋮ Eigenvectors and controllability of non-Hermitian random matrices and directed graphs ⋮ \(L^p\) norms and support of eigenfunctions on graphs ⋮ Quantum ergodicity on graphs: from spectral to spatial delocalization ⋮ Quantum ergodicity on large regular graphs

Cites Work

• Quantum ergodicity on large regular graphs
• Resonant delocalization for random Schrödinger operators on tree graphs
• Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs
• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs
• An Introduction to Random Matrices
• LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS
• Unnamed Item

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