Normal typicality and dynamical typicality for a random block-band matrix model
Erdös L, Henheik SJ, Vogel C. 2026. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 116, 5.
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Abstract
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices (Erdős and Riabov in Commun Math Phys 405(12): 282, 2024) and an intricate analysis of the deterministic approximation.
Publishing Year
Date Published
2026-02-01
Journal Title
Letters in Mathematical Physics
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Springer Nature
Acknowledgement
L.E. and J.H. are supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. Moreover, J.H. acknowledges (partial) financial support by the ERC Consolidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education, Research and Innovation). C.V. was (partially) supported by the German Academic Scholarship Foundation and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – TRR 352 – Project-ID 470903074. Moreover, C.V. acknowledges (partial) financial support by the ERC Starting Grant “FermiMath" No. 101040991 and the ERC Consolidator Grant “RAMBAS” No. 10104424, funded by the European Union. Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
116
Article Number
5
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eISSN
IST-REx-ID
Cite this
Erdös L, Henheik SJ, Vogel C. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 2026;116. doi:10.1007/s11005-025-02037-5
Erdös, L., Henheik, S. J., & Vogel, C. (2026). Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-02037-5
Erdös, László, Sven Joscha Henheik, and Cornelia Vogel. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics. Springer Nature, 2026. https://doi.org/10.1007/s11005-025-02037-5.
L. Erdös, S. J. Henheik, and C. Vogel, “Normal typicality and dynamical typicality for a random block-band matrix model,” Letters in Mathematical Physics, vol. 116. Springer Nature, 2026.
Erdös L, Henheik SJ, Vogel C. 2026. Normal typicality and dynamical typicality for a random block-band matrix model. Letters in Mathematical Physics. 116, 5.
Erdös, László, et al. “Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model.” Letters in Mathematical Physics, vol. 116, 5, Springer Nature, 2026, doi:10.1007/s11005-025-02037-5.
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