Mariya Shcherbina, Tatyana Shcherbina
Published 2019-05-20Version 1
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation functions). We show that when the bandwidth $W$ crosses the threshold $W=N^{1/2}$, the model has a kind of phase transition (crossover), whose nature can be explained by the spectral properties of the transfer operator.
Comments: 19p. arXiv admin note: substantial text overlap with arXiv:1802.03813
Journal: Proc. Int. Cong. of Math., Vol 2, 2018
Characteristic polynomials for 1D random band matrices from the localization side
Characteristic polynomials for random band matrices near the threshold
Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$
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