Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Ducatez, Raphael"'
Autor:
Ducatez, Raphael
We propose a new random process to construct the eigenvectors of some random operators which make a short and clean connection with the resolvent. In this process the center of localization has to be chosen randomly.
Externí odkaz:
http://arxiv.org/abs/2406.07035
We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that $H_{ij}^{N}=\frac{1}{\sqrt{N}}X_{i
Externí odkaz:
http://arxiv.org/abs/2403.05413
Autor:
Ducatez, Raphael, Rivier, Renaud
For the Erd\H{o}s-R\'enyi graph of size $N$ with mean degree $(1+o(1))\frac{\log N}{t+1}\leq d\leq(1-o(1))\frac{\log N}{t}$ where $t\in\mathbb{N}^{*}$, with high probability the smallest non zero eigenvalue of the Laplacian is equal to $2-2\cos(\pi(2
Externí odkaz:
http://arxiv.org/abs/2309.17292
Autor:
Ducatez, Raphael
This is a short introduction of the exterior form formalism focus on its applications in physics and then mostly aimed to physics students. As a rule of a game played here we never use a coordinate frame neither in the definitions nor in the proofs b
Externí odkaz:
http://arxiv.org/abs/2307.06597
We analyse the eigenvectors of the adjacency matrix of the Erd\H{o}s-R\'enyi graph $\mathbb G(N,d/N)$ for $\sqrt{\log N} \ll d \lesssim \log N$. We show the existence of a localized phase, where each eigenvector is exponentially localized around a si
Externí odkaz:
http://arxiv.org/abs/2305.16294
We establish precise upper-tail asymptotics and large deviation principles for the rightmost eigenvalue $\lambda_1$ of Wigner matrices with sub-Gaussian entries. In contrast to the case of heavier tails, where deviations of $\lambda_1$ are due to the
Externí odkaz:
http://arxiv.org/abs/2302.14823
We analyse the eigenvectors of the adjacency matrix of the Erd\H{o}s-R\'enyi graph on $N$ vertices with edge probability $\frac{d}{N}$. We determine the full region of delocalization by determining the critical values of $\frac{d}{\log N}$ down to wh
Externí odkaz:
http://arxiv.org/abs/2109.03227
We consider the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph on $N$ vertices with edge probability $d/N$. For $(\log \log N)^4 \ll d \lesssim \log N$, we prove that the eigenvalues near the spectral edge form asymptotically a Poisson process a
Externí odkaz:
http://arxiv.org/abs/2106.12519
We analyse the eigenvectors of the adjacency matrix of a critical Erd\H{o}s-R\'enyi graph $\mathbb G(N,d/N)$, where $d$ is of order $\log N$. We show that its spectrum splits into two phases: a delocalized phase in the middle of the spectrum, where t
Externí odkaz:
http://arxiv.org/abs/2005.14180
We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph $G(N,d/N)$ in the critical regime $d \asymp \log N$ of the transition uncovered in [arXiv:1704.02953,arXiv:1704.02945], where the regi
Externí odkaz:
http://arxiv.org/abs/1905.03243