Kevin Yang

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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…

math.PR2024

Bulk universality for complex eigenvalues of real non-symmetric random matrices with i.i.d. entries

Sofiia Dubova, Kevin Yang

We consider an ensemble of non-Hermitian matrices with independent identically distributed real entries that have finite moments. We show that its $k$ -point correlation function in…