Evidence of the Poisson/Gaudin–Mehta phase transition for band matrices on global scales

DOI10.1142/S2010326318500028zbMath1392.60014arXiv1703.06985OpenAlexW4255127415MaRDI QIDQ4568314

Andrew Swan, Sheehan Olver

Publication date: 19 June 2018

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06985

zbMATH Keywords

random band matrixAnderson transitionglobal statisticsPoisson/Gaudin-Mehta transition

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52)

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Circular law for random block band matrices with genuinely sublinear bandwidth

Cites Work

• Delocalization and diffusion profile for random band matrices
• Characteristic polynomials for 1D random band matrices from the localization side
• Delocalization for a class of random block band matrices
• Quantum diffusion and eigenfunction delocalization in a random band matrix model
• The spectral edge of some random band matrices
• Eigenvector localization for random band matrices with power law band width
• On the level density of random band matrices
• Limiting eigenvalue distribution for band random matrices
• Universality for a class of random band matrices
• The Altshuler-Shklovskii formulas for random band matrices. II: The general case
• On the second mixed moment of the characteristic polynomials of 1D band matrices
• Universality of the local regime for the block band matrices with a finite number of blocks
• The Altshuler-Shklovskii formulas for random band matrices. I: The unimodular case
• Scaling properties of localization in random band matrices: A σ-model approach