H. Yau

activity

19992026

most citedDerivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems

344 citations · 3.1k across the 86 of their papers we have counts for

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Showing 2025 · math.PRShow all

4 papers · 2 filters

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.PR2025

Gaussian Waves and Edge Eigenvectors of Random Regular Graphs

Yukun He, Jiaoyang Huang, Horng-Tzer Yau

Backhausz and Szegedy (2019) demonstrated that the almost eigenvectors of random regular graphs converge to Gaussian waves with variance $0 \leq σ^{2} \leq 1$ . In this paper, we presen…

math.PR2025★ 1 cited

Delocalization of One-Dimensional Random Band Matrices

Horng-Tzer Yau, Jun Yin

Consider an $N \times N$ Hermitian one-dimensional random band matrix with band width $W > N^{1/2 + c}$ for any $c > 0$ . In the bulk of the spectrum and in the l…

Delocalization of Non-Mean-Field Random Matrices in Dimensions d≥3

Delocalization of Two-Dimensional Random Band Matrices

Gaussian Waves and Edge Eigenvectors of Random Regular Graphs

Delocalization of One-Dimensional Random Band Matrices

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