Patrick Lopatto

collaborators

3 papers

math.NT2024

Formulas for odd zeta values and powers of $π$

Marc Chamberland, Patrick Lopatto

Plouffe conjectured rapidly converging series formulas for $π^{2 n + 1}$ and $ζ (2 n + 1)$ for small values of $n$ . We find the general pattern for all nonnegative integer values of $n$ a…

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…

Formulas for odd zeta values and powers of π

Smallest gaps between eigenvalues of real Gaussian matrices

Quenched large deviation principles for random projections of ℓpn​ balls

Formulas for odd zeta values and powers of $π$

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