48 citations · 205 across the 13 of their papers we have counts for
17 papers
Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation
Lucas Morisset, Alain Durmus, Adrien Hardy
This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates gr…
Non-Asymptotic Analysis of Data Augmentation for Precision Matrix Estimation
Lucas Morisset, Adrien Hardy, Alain Durmus
This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators…
From point processes to quantum optics and back
Rémi Bardenet, Alexandre Feller, Jérémie Bouttier +6
Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of…
CLT for Circular beta-Ensembles at High Temperature
Adrien Hardy, Gaultier Lambert
We consider the macroscopic large N limit of the Circular beta-Ensemble at high temperature, and its weighted version as well, in the regime where the inverse temperature scales as…
Mutual Information of Wireless Channels and Block-Jacobi Ergodic Operators
Walid Hachem, Adrien Hardy, Shlomo Shamai
Shannon's mutual information of a random multiple antenna and multipath channel is studied in the general case where the channel impulse response is an ergodic and stationary proce…
DLR equations and rigidity for the Sine-beta process
David Dereudre, Adrien Hardy, Thomas Leblé +1
We investigate Sine, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or -ensembles…
Time-frequency transforms of white noises and Gaussian analytic functions
Rémi Bardenet, Adrien Hardy
A family of Gaussian analytic functions (GAFs) has recently been linked to the Gabor transform of white Gaussian noise [Bardenet et al., 2017]. This answered pioneering work by Fla…
Energy of the Coulomb gas on the sphere at low temperature
Carlos Beltrán, Adrien Hardy
We consider the Coulomb gas of particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order …
Polynomial Ensembles and Recurrence Coefficients
Adrien Hardy
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put…
Concentration for Coulomb gases and Coulomb transport inequalities
Djalil Chafai, Adrien Hardy, Mylène Maïda
We study the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are modeled by an exchangeable Boltzmann-Gibbs measure with a singular two-body interact…
Monte Carlo with Determinantal Point Processes
Rémi Bardenet, Adrien Hardy
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical , where is the number of integrand evaluations. M…
A Survey on the Eigenvalues Local Behavior of Large Complex Correlated Wishart Matrices
Walid Hachem, Adrien Hardy, Jamal Najim
The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues…
Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge
Walid Hachem, Adrien Hardy, Jamal Najim
We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine t…
Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges
Walid Hachem, Adrien Hardy, Jamal Najim
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eig…
Average Characteristic Polynomials of Determinantal Point Processes
Adrien Hardy
We investigate the average characteristic polynomial where the 's are real random variables which form a determinantal point process…
Large Deviations for a Non-Centered Wishart Matrix
Adrien Hardy, Arno B. J. Kuijlaars
We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associat…
A Note on Large Deviations for 2D Coulomb Gas with Weakly Confining Potential
Adrien Hardy
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence t…