Patrick Lopatto

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math.PR2024

Smallest gaps between eigenvalues of real Gaussian matrices

Patrick Lopatto, Matthew Meeker

We consider an $n \times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.

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…

Smallest gaps between eigenvalues of real Gaussian matrices

Quenched large deviation principles for random projections of ℓpn​ balls

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