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<p>We prove <i>normal typicality</i> and <i>dynamical typicality</i> 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.</p>

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Normal typicality and dynamical typicality for a random block-band matrix model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月26日

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  • László Erdős,
  • Joscha Henheik,
  • Cornelia Vogel

摘要

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.