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

collaborators

Showing 2021 · math.PRShow all

3 papers · 2 filters

math.PR2021★ 9 cited

Delocalization and quantum diffusion of random band matrices in high dimensions II: $T$ -expansion

Fan Yang, Horng-Tzer Yau, Jun Yin

We consider Green's functions $G (z) := (H - z)^{- 1}$ of Hermitian random band matrices $H$ on the $d$ -dimensional lattice $(Z / L Z)^{d}$ . The entries $h_{x y} = h ˉ_{y x}$ o…

math.PR2021

Delocalization and quantum diffusion of random band matrices in high dimensions I: Self-energy renormalization

Fan Yang, Horng-Tzer Yau, Jun Yin

We consider Hermitian random band matrices $H = (h_{x y})$ on the $d$ -dimensional lattice $(Z / L Z)^{d}$ . The entries $h_{x y}$ are independent (up to Hermitian conditions)…

math.PR2021★ 7 cited

Spectrum of Random $d$ -regular Graphs Up to the Edge

Jiaoyang Huang, Horng-Tzer Yau

Consider the normalized adjacency matrices of random $d$ -regular graphs on $N$ vertices with fixed degree $d \geq 3$ . We prove that, with probability $1 - N^{- 1 + ε}$ for any…

Delocalization and quantum diffusion of random band matrices in high dimensions II: T-expansion

Delocalization and quantum diffusion of random band matrices in high dimensions I: Self-energy renormalization

Spectrum of Random d-regular Graphs Up to the Edge

Delocalization and quantum diffusion of random band matrices in high dimensions II: $T$ -expansion

Spectrum of Random $d$ -regular Graphs Up to the Edge