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- W4318719504 abstract "We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random potential. This article is devoted to their spectral statistics. We show that the rescaled spectrum converges to the clock process for fast decay and to the Schrodinger/Sine processes from random matrix theory for critical decay. This way, we recover all the regimes previously identified for the Anderson model in a similar context [25]. Poisson statistics, which should appear in the model with slow decay, are left as an open problem. The core of the proof consists in a suitable scaling limit for the Prufer phase and monotonicity arguments, yielding an alternative to the approach of [25]. For one of the models, we also obtain the scaling limit of the Prufer radii and discuss the consequences for the limiting shape of the eigenfunctions." @default.
- W4318719504 created "2023-02-01" @default.
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- W4318719504 date "2023-01-30" @default.
- W4318719504 modified "2023-10-09" @default.
- W4318719504 title "One-dimensional Discrete Dirac Operators in a Decaying Random Potential II: Clock, Schrodinger and Sine statistics" @default.
- W4318719504 doi "https://doi.org/10.48550/arxiv.2301.13107" @default.
- W4318719504 hasPublicationYear "2023" @default.
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