Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Potters, Marc"'
The study of eigenvalue distributions in random matrix theory is often conducted by analyzing the resolvent matrix $ \mathbf{G}_{\mathbf{M}}^N(z) = (z \mathbf{1} - \mathbf{M})^{-1} $. The normalized trace of the resolvent, known as the Stieltjes tran
Externí odkaz:
http://arxiv.org/abs/2411.19266
Autor:
Bousseyroux, Pierre, Potters, Marc
We explore a spectral initialization method that plays a central role in contemporary research on signal estimation in nonconvex scenarios. In a noiseless phase retrieval framework, we precisely analyze the method's performance in the high-dimensiona
Externí odkaz:
http://arxiv.org/abs/2403.15548
Using Random Matrix Theory, we propose a universal and versatile tool to reveal the existence of "fleeting modes", i.e. portfolios that carry statistically significant excess risk, signalling ex-post a change in the correlation structure in the under
Externí odkaz:
http://arxiv.org/abs/2205.01012
Autor:
Mergny, Pierre, Potters, Marc
In this note we study the right large deviation of the top eigenvalue (or singular value) of the sum or product of two random matrices $\mathbf{A}$ and $\mathbf{B}$ as their dimensions goes to infinity. The matrices $\mathbf{A}$ and $\mathbf{B}$ are
Externí odkaz:
http://arxiv.org/abs/2201.11836
Autor:
Mergny, Pierre, Potters, Marc
Publikováno v:
SciPost Phys. 12, 022 (2022)
We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where $\frac{N \beta}{2} \to c $, called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter $c$ betwe
Externí odkaz:
http://arxiv.org/abs/2101.01810
Autor:
Bouchaud, Jean-Philippe, Potters, Marc
Publikováno v:
Phys. Rev. E 102, 062117 (2020)
We study the spectrum of generalized Wishart matrices, defined as $\mathbf{F}=( X Y^\top + Y X^\top)/2T$, where $X$ and $Y$ are $N \times T$ matrices with zero mean, unit variance IID entries and such that $\mathbb{E}[X_{it} Y_{jt}]=c \delta_{i,j}$.
Externí odkaz:
http://arxiv.org/abs/2009.07113
Autor:
Mergny, Pierre, Potters, Marc
In this note, we study the asymptotic of spherical integrals, which are analytical extension in index of the normalized Schur polynomials for $\beta =2$ , and of Jack symmetric polynomials otherwise. Such integrals are the multiplicative counterparts
Externí odkaz:
http://arxiv.org/abs/2007.09421
We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is large but $
Externí odkaz:
http://arxiv.org/abs/1901.05543