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arXiv · 1808.07106

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

Vlad Margarint
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Abstract

We consider Hermitian random band matrices $H$ in $d \geq 1 $ dimensions. The matrix elements $H_{xy},$ indexed by $x, y \in \Lambda \subset \mathbb{Z}^d,$ are independent, uniformly distributed random variable if $|x-y| $ is less than the band width $W,$ and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size $|\Lambda| $ of the matrix.

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Vlad Margarint. 2018-08-21. Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model. https://doi.org/10.1007/s10955-018-2065-2

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