Abstract
We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by J=(-W2▵+1)-1. Assuming that the band width W≪n, we prove that the limit of the normalized second mixed moment of characteristic polynomials (as W, n→ ∞) is equal to one, and so it does not coincide with that for GUE. This complements the result of Shcherbina (J Stat Phys 155(3):466–499, 2014) and proves the existence of the expected crossover for 1D Hermitian random band matrices at W∼n on the level of characteristic polynomials.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1009-1044 |
| Number of pages | 36 |
| Journal | Communications In Mathematical Physics |
| Volume | 351 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2017 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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Shcherbina, M., & Shcherbina, T. (2017). Characteristic Polynomials for 1D Random Band Matrices from the Localization Side. Communications In Mathematical Physics, 351(3), 1009-1044. https://doi.org/10.1007/s00220-017-2849-2