Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Coste Simon"'
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 74, Pp 137-157 (2023)
We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrice
Externí odkaz:
https://doaj.org/article/b53f5402e382439bb01a09b5a3812172
We analyse the numbers of closed paths of length $k\in\mathbb{N}$ on two important regular lattices: the hexagonal lattice (also called $\textit{graphene}$ in chemistry) and its dual triangular lattice. These numbers form a moment sequence of specifi
Externí odkaz:
http://arxiv.org/abs/2306.01462
Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to the data d
Externí odkaz:
http://arxiv.org/abs/2305.19414
Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs
Externí odkaz:
http://arxiv.org/abs/2208.05003
Let $A_n$ be the sum of $d$ permutation matrices of size $n\times n$, each drawn uniformly at random and independently. We prove that the normalized characteristic polynomial $\frac{1}{\sqrt{d}}\det(I_n - z A_n/\sqrt{d})$ converges when $n\to \infty$
Externí odkaz:
http://arxiv.org/abs/2204.00524
Autor:
Coste, Simon
We prove that the reverse characteristic polynomial $\det(I_n - zA_n)$ of a random $n \times n$ matrix $A_n$ with iid $\mathrm{Bernoulli}(d/n)$ entries converges in distribution towards the random infinite product $\prod_{\ell = 1}^\infty(1-z^\ell)^{
Externí odkaz:
http://arxiv.org/abs/2106.00593
Autor:
Coste, Simon, Stephan, Ludovic
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD truncation, a
Externí odkaz:
http://arxiv.org/abs/2102.03188
Let $A$ be a rectangular matrix of size $m\times n$ and $A_1$ be the random matrix where each entry of $A$ is multiplied by an independent $\{0,1\}$-Bernoulli random variable with parameter $1/2$. This paper is about when, how and why the non-Hermiti
Externí odkaz:
http://arxiv.org/abs/2005.06062
Akademický článek
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Autor:
Coste, Simon, Zhu, Yizhe
Publikováno v:
Random Matrices: Theory and Applications, 10(3), 2150028, 2021
We describe the non-backtracking spectrum of a stochastic block model with connection probabilities $p_{\mathrm{in}}, p_{\mathrm{out}} = \omega(\log n)/n$. In this regime we answer a question posed in Dall'Amico and al. (2019) regarding the existence
Externí odkaz:
http://arxiv.org/abs/1907.05603