Sofiia Dubova

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math.PR2025

Delocalization of Non-Mean-Field Random Matrices in Dimensions $d \geq 3$

Sofiia Dubova, Fan Yang, Horng-Tzer Yau +1

We study $N \times N$ random band matrices $H = (H_{x y})$ with mean-zero complex Gaussian entries, where $x, y$ lie on the discrete torus $(Z / d N Z)^{d}$ i…

math.PR2025

Delocalization of Two-Dimensional Random Band Matrices

Sofiia Dubova, Kevin Yang, Horng-Tzer Yau +1

We study a random band matrix $H = (H_{x y})_{x, y}$ of dimension $N \times N$ with mean-zero complex Gaussian entries, where $x, y$ belong to the discrete torus $(\mathbb{Z}/\sqrt{N}\ma…

math.PR2024

Quantum diffusion and delocalization in one-dimensional band matrices via the flow method

Sofiia Dubova, Kevin Yang

We study a class of Gaussian random band matrices of dimension $N \times N$ and band-width $W$ . We show that delocalization holds for bulk eigenvectors and that quantum diffusion h…