Horng‐Tzer Yau

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math-ph2009★ 23 cited

Bulk Universality for Wigner Matrices

Laszlo Erdos, Sandrine Peche, Jose A. Ramirez +2

We consider $N \times N$ Hermitian Wigner random matrices $H$ where the probability density for each matrix element is given by the density $ν (x) = e^{- U (x)}$ . We prove that the eig…

math-ph2009★ 116 cited

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Horng-Tzer Yau, Jun Yin

Consider $N$ bosons in a finite box $Λ = [0, L]^{3} \subset R^{3}$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives…

math-ph2008★ 30 cited

Wegner estimate and level repulsion for Wigner random matrices

Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau

We consider $N \times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing betwee…