22 citations · 30 across the 31 of their papers we have counts for
5 papers · 1 filter
Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices
Paul Bourgade, Patrick Lopatto, Ofer Zeitouni
We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and -ensembles. In the special case of Gaussian-divisible Wigner matrices, our met…
Quenched large deviation principles for random projections of balls
Patrick Lopatto, Kavita Ramanan, Xiaoyu Xie
Let be a sequence of positive integers growing to infinity at a sublinear rate, and as $n \rightarrow \inf…
Central limit theorem for the complex eigenvalues of Gaussian random matrices
Advay Goel, Patrick Lopatto, Xiaoyu Xie
We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.
Fast computation of exact confidence intervals for randomized experiments with binary outcomes
P. M. Aronow, Haoge Chang, Patrick Lopatto
Given a randomized experiment with binary outcomes, exact confidence intervals for the average causal effect of the treatment can be computed through a series of permutation tests.…
Fluctuations in Quantum Unique Ergodicity at the Spectral Edge
Lucas Benigni, Nixia Chen, Patrick Lopatto +1
We study the eigenvector mass distribution of an Wigner matrix on a set of coordinates satisfying for some constant . For eigenvectors corresp…