ABSOLUTELY CONTINUOUS SPECTRUM FOR A RANDOM POTENTIAL ON A TREE WITH STRONG TRANSVERSE CORRELATIONS AND LARGE WEIGHTED LOOPS

DOI10.1142/S0129055X09003724zbMath1168.82315arXiv0809.4197MaRDI QIDQ3395532

David Hasler, Richard Froese, Wolfgang L. Spitzer

Publication date: 5 September 2009

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.4197

zbMATH Keywords

absolutely continuous spectrumBethe lattice with spherical mean field Laplacianstrongly correlated random potential

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes, Anderson transition at two-dimensional growth rate on antitrees and spectral theory for operators with one propagating channel, Absolutely continuous spectrum for random operators on trees of finite cone type, Absolutely continuous spectrum for the Anderson model on some tree-like graphs, Absolutely continuous spectrum for random Schrödinger operators on tree-strips of finite cone type, Ballistic behavior for random Schrödinger operators on the Bethe strip, Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph, Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar tree-strips

Cites Work

• Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs
• Absolutely continuous spectrum for the Anderson model on a tree: a geometric proof of Klein's theorem
• Singular continuous spectrum for the Laplacian on certain sparse trees
• Absolutely continuous spectra of quantum tree graphs with weak disorder
• Extended states in the Anderson model on the Bethe lattice
• The Canophy graph and level statistics for random operators on trees
• Localization for the Anderson model on trees with finite dimensions
• Stability of the absolutely continuous spectrum of random Schrödinger operators on tree graphs