Ji Oon Lee

Rate of Convergence Towards Hartree Dynamics

We consider a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schrödinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.

A necessary and sufficient condition for edge universality of Wigner matrices

In this paper, we prove a necessary and sufficient condition for Tracy-Widom law of Wigner matrices. Consider

Bulk universality for deformed Wigner matrices

N times N

Tracy–Widom distribution for the largest eigenvalue of real sample covariance matrices with general population.

symmetric Wigner matrices

Local deformed semicircle law and complete delocalization for Wigner matrices with random potential

H

Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model

with

Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

H_{ij} = N^{-1/2} x_{ij}

Edge universality for deformed Wigner matrices

, whose upper right entries

Rate of convergence in nonlinear Hartree dynamics with factorized initial data

x_{ij}