Xiaoyu Xie

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math.PR2024

The $ℓ_{r}$ -Levy-Grothendieck problem and $r \to p$ norms of Levy matrices

Kavita Ramanan, Xiaoyu Xie

Given an $n \times n$ matrix $A_{n}$ and $1 \leq r, p \leq \infty$ , consider the following quadratic optimization problem referred to as the $ℓ_{r}$ -Grothendieck problem: \begin{align}…

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…

The ℓr​-Levy-Grothendieck problem and r→p norms of Levy 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

The $ℓ_{r}$ -Levy-Grothendieck problem and $r \to p$ norms of Levy matrices

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