Zobrazeno 1 - 10
of 91
pro vyhledávání: '"Schnelli, Kevin"'
Autor:
Parraud, Félix, Schnelli, Kevin
In this paper we study multi-matrix models whose potentials are small perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials
Externí odkaz:
http://arxiv.org/abs/2310.12948
Autor:
Parraud, Félix, Schnelli, Kevin
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on minimizing the assu
Externí odkaz:
http://arxiv.org/abs/2208.02118
Autor:
Schnelli, Kevin, Xu, Yuanyuan
We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix $H$ converge to the Tracy-Widom laws at a rate nearly $O(N^{-1/3})$, as the matrix dimension $N$ tends to infinity. We allow the variances of the entries of $H$
Externí odkaz:
http://arxiv.org/abs/2207.00546
Autor:
Moreillon, Philippe, Schnelli, Kevin
We consider the free additive convolution $\mu_\alpha\boxplus\mu_\beta$ of two probability measures $\mu_\alpha$ and $\mu_\beta$, supported on respectively $n_\alpha$ and $n_\beta$ disjoint bounded intervals on the real line, and derive a lower bound
Externí odkaz:
http://arxiv.org/abs/2201.05582
Autor:
Parraud, Félix, Schnelli, Kevin
Publikováno v:
In Linear Algebra and Its Applications 15 October 2024 699:1-46
Autor:
Schnelli, Kevin, Xu, Yuanyuan
We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix $X^*X$ converg
Externí odkaz:
http://arxiv.org/abs/2108.02728
Autor:
Schnelli, Kevin, Xu, Yuanyuan
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+\omega})$, as $N$ tends to infinity. For Wigner matrices this improves t
Externí odkaz:
http://arxiv.org/abs/2102.04330
Publikováno v:
Forum of Mathematics, Sigma 9 (2021) e44
We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principl
Externí odkaz:
http://arxiv.org/abs/2008.07061
We consider random matrices of the form $H_N=A_N+U_N B_N U^*_N$, where $A_N$, $B_N$ are two $N$ by $N$ deterministic Hermitian matrices and $U_N$ is a Haar distributed random unitary matrix. We establish a universal Central Limit Theorem for the line
Externí odkaz:
http://arxiv.org/abs/2001.07661
We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central Limit Theorem
Externí odkaz:
http://arxiv.org/abs/1909.12821