P. Lopatto

activity

20142026

most citedFluctuations in local quantum unique ergodicity for generalized Wigner matrices

22 citations · 30 across the 31 of their papers we have counts for

collaborators

Showing 2023 · math.PRShow all

4 papers · 2 filters

math.PR2023★ 1 cited

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 $β$ -ensembles. In the special case of Gaussian-divisible Wigner matrices, our met…

math.PR2023

Quenched large deviation principles for random projections of $ℓ_{p}^{n}$ balls

Patrick Lopatto, Kavita Ramanan, Xiaoyu Xie

Let $(k_{n})_{n \in N}$ be a sequence of positive integers growing to infinity at a sublinear rate, $k_{n} \to \infty$ and $k_{n} / n \to 0$ as $n \rightarrow \inf…

math.PR2023

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.

math.PR2023

Fluctuations in Quantum Unique Ergodicity at the Spectral Edge

Lucas Benigni, Nixia Chen, Patrick Lopatto +1

We study the eigenvector mass distribution of an $N \times N$ Wigner matrix on a set of coordinates $I$ satisfying $∣ I ∣ \geq c N$ for some constant $c > 0$ . For eigenvectors corresp…

Optimal rigidity and maximum of the characteristic polynomial of Wigner matrices

Quenched large deviation principles for random projections of ℓpn​ balls

Central limit theorem for the complex eigenvalues of Gaussian random matrices

Fluctuations in Quantum Unique Ergodicity at the Spectral Edge

Quenched large deviation principles for random projections of $ℓ_{p}^{n}$ balls