8 papers · 1 filter
Operator level soft edge to bulk transition in -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…
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…
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…
Bulk asymptotics of the Gaussian -ensemble characteristic polynomial
Gaultier Lambert, Elliot Paquette
The Gaussian -ensemble (GE) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomia…
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…
The extremal landscape for the CE ensemble
Elliot Paquette, Ofer Zeitouni
We consider the extremes of the logarithm of the characteristic polynomial of matrices from the CE ensemble. We prove convergence in distribution of the centered maxima (of the…