Elliot Paquette

activity

20082026

most citedFunctional limit theorems for random regular graphs

33 citations · 133 across the 43 of their papers we have counts for

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34 papers · 1 filter

math.PR2026

Anisotropic local law for non-separable sample covariance matrices

Zhou Fan, Renyuan Ma, Elliot Paquette +1

We establish local laws for sample covariance matrices $K = N^{-1}\sum_{i=1}^N \g_i\g_i^*$ where the random vectors $\g_1, \ldots, \g_N \in \R^n$ are independent with common covari…

math.PR2025

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling

Lucas Benigni, Elliot Paquette

We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\ti…

math.PR2025

Bulk asymptotics of the Gaussian $β$ -ensemble characteristic polynomial

Gaultier Lambert, Elliot Paquette

The Gaussian $β$ -ensemble (G $β$ E) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomial…

math.PR2025

The Fourier coefficients of the holomorphic multiplicative chaos in the limit of large frequency

Joseph Najnudel, Elliot Paquette, Nick Simm +1

The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characterist…

math.PR2025

Operator level soft edge to bulk transition in $β$ -ensembles via canonical systems

Vincent Painchaud, Elliot Paquette

The stochastic Airy and sine operators, which are respectively a random Sturm-Liouville operator and a random Dirac operator, characterize the soft edge and bulk scaling limits of…

math.PR2024

The image of random analytic functions: coverage of the complex plane via branching processes

Alon Nishry, Elliot Paquette

We consider the range of random analytic functions with finite radius of convergence. We show that any unbounded random Taylor series with rotationally invariant coefficients has d…

math.PR2023★ 1 cited

Fitting an ellipsoid to a quadratic number of random points

Afonso S. Bandeira, Antoine Maillard, Shahar Mendelson +1

We consider the problem $(P)$ of fitting $n$ standard Gaussian random vectors in $R^{d}$ to the boundary of a centered ellipsoid, as $n, d \to \infty$ . This problem…

math.PR2023

High-dimensional limit of one-pass SGD on least squares

Elizabeth Collins-Woodfin, Elliot Paquette

We give a description of the high-dimensional limit of one-pass single-batch stochastic gradient descent (SGD) on a least squares problem. This limit is taken with non-vanishing st…

math.PR2022★ 1 cited

The extremal landscape for the C $β$ E ensemble

Elliot Paquette, Ofer Zeitouni

We consider the extremes of the logarithm of the characteristic polynomial of matrices from the C $β$ E ensemble. We prove convergence in distribution of the centered maxima (of the…

math.PR2021

Random geometric graphs and the spherical Wishart matrix

Elliot Paquette, Andrew Vander Werf

We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$ --dimensional sphere. We focus on the sparse regime, when the expected degree is constant independe…

math.PR2020★ 5 cited

Secular Coefficients and the Holomorphic Multiplicative Chaos

Joseph Najnudel, Elliot Paquette, Nick Simm

We study the secular coefficients of $N \times N$ random unitary matrices $U_{N}$ drawn from the Circular $β$ -Ensemble, which are defined as the coefficients of ${z^{n}}$ in the ch…

math.PR2020★ 7 cited

Strong approximation of Gaussian $β$ -ensemble characteristic polynomials: the edge regime and the stochastic Airy function

Gaultier Lambert, Elliot Paquette

We investigate the characteristic polynomials of the Gaussian $β$ -ensemble for general $β > 0$ through its transfer matrix recurrence. We show that the rescaled characteristic polyno…

math.PR2020

Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes

Itai Benjamini, Yoav Krauz, Elliot Paquette

We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is a bounded mean densi…

math.PR2020

Interval fragmentations with choice: equidistribution and the evolution of tagged fragments

Pascal Maillard, Elliot Paquette

We consider a Markovian evolution on point processes, the $Ψ$ --process, on the unit interval in which points are added according to a rule that depends only on the spacings of the…

math.PR2020★ 2 cited

Strong approximation of Gaussian beta-ensemble characteristic polynomials: the hyperbolic regime

Gaultier Lambert, Elliot Paquette

We investigate the characteristic polynomials $φ_{N}$ of the Gaussian $β$ -ensemble for general $β > 0$ through its transfer matrix recurrence. Our motivation is to obtain a (probabilis…

math.PR2019

On the speed of distance stationary sequences

Matias Carrasco, Pablo Lessa, Elliot Paquette

We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formul…

math.PR2018

Spectrum of random perturbations of Toeplitz matrices with finite symbols

Anirban Basak, Elliot Paquette, Ofer Zeitouni

Let $T_{N}$ denote an $N \times N$ Toeplitz matrix with finite, $N$ independent symbol $a$ . For $E_{N}$ a noise matrix satisfying mild assumptions (ensuring, in particular, that $…

math.PR2018★ 1 cited

The maximum deviation of the Sine $_{β}$ counting process

Diane Holcomb, Elliot Paquette

In this paper, we consider the maximum of the $Sine_{β}$ counting process from its expectation. We show the leading order behavior is consistent with the predictions of log-co…

math.PR2017

Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases

Anirban Basak, Elliot Paquette, Ofer Zeitouni

We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_{N}$ be a deterministic $N \times N$ matrix, and let $G…

math.PR2017★ 3 cited

A Furstenberg type formula for the speed of distance stationary sequences

Matias Carrasco, Pablo Lessa, Elliot Paquette

We prove a formula for the speed of distance stationary random sequences. A particular case is the classical formula for the largest Lyapunov exponent of an i.i.d. product of two b…

math.PR2017★ 2 cited

Tridiagonal Models for Dyson Brownian Motion

Diane Holcomb, Elliot Paquette

In this paper, we consider tridiagonal matrices the eigenvalues of which evolve according to $β$ -Dyson Brownian motion. This is the stochastic gradient flow on $R^{n}$ given…

math.PR2017

Distributional Lattices on Riemannian symmetric spaces

Elliot Paquette

A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the…

math.PR2016★ 5 cited

The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matrices

Gaultier Lambert, Elliot Paquette

We compute the leading asymptotics as $N \to \infty$ of the maximum of the field $Q_{N} (q) = lo g det ∣ q - A_{N} ∣$ , $q \in C$ , for any unitarily invariant Hermitian random matrix $A…

math.PR2016

The maximum of the CUE field

Elliot Paquette, Ofer Zeitouni

Let $U_{N}$ denote a Haar Unitary matrix of dimension N, and consider the field \[ {\bf U}(z) = \log |\det(1-zU_N)| \] for z in the unit disk. Then, \[ \frac{\max_{|z|=1} {\bf U}(z)…

Anisotropic local law for non-separable sample covariance matrices

Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling

Bulk asymptotics of the Gaussian β-ensemble characteristic polynomial

The Fourier coefficients of the holomorphic multiplicative chaos in the limit of large frequency

Operator level soft edge to bulk transition in β-ensembles via canonical systems

The image of random analytic functions: coverage of the complex plane via branching processes

Fitting an ellipsoid to a quadratic number of random points

High-dimensional limit of one-pass SGD on least squares

The extremal landscape for the CβE ensemble

Random geometric graphs and the spherical Wishart matrix

Secular Coefficients and the Holomorphic Multiplicative Chaos

Strong approximation of Gaussian β-ensemble characteristic polynomials: the edge regime and the stochastic Airy function

Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes

Interval fragmentations with choice: equidistribution and the evolution of tagged fragments

Strong approximation of Gaussian beta-ensemble characteristic polynomials: the hyperbolic regime

On the speed of distance stationary sequences

Spectrum of random perturbations of Toeplitz matrices with finite symbols

The maximum deviation of the Sineβ​ counting process

Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases

A Furstenberg type formula for the speed of distance stationary sequences

Tridiagonal Models for Dyson Brownian Motion

Distributional Lattices on Riemannian symmetric spaces

The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matrices

The maximum of the CUE field

Bulk asymptotics of the Gaussian $β$ -ensemble characteristic polynomial

Operator level soft edge to bulk transition in $β$ -ensembles via canonical systems

The extremal landscape for the C $β$ E ensemble

Strong approximation of Gaussian $β$ -ensemble characteristic polynomials: the edge regime and the stochastic Airy function

The maximum deviation of the Sine $_{β}$ counting process