Zobrazeno 1 - 10
of 252
pro vyhledávání: '"BORDENAVE, CHARLES"'
Toeplitz matrices form a rich class of possibly non-normal matrices whose asymptotic spectral analysis in high dimension is well-understood. The spectra of these matrices are notoriously highly sensitive to small perturbations. In this work, we analy
Externí odkaz:
http://arxiv.org/abs/2410.16439
We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries per row.
Externí odkaz:
http://arxiv.org/abs/2409.14027
Autor:
Bonnin, Remi, Bordenave, Charles
We pursue the current developments in random tensor theory by laying the foundations of a free probability theory for tensors and establish its relevance in the study of random tensors of high dimension. We give a definition of freeness associated to
Externí odkaz:
http://arxiv.org/abs/2407.18881
Autor:
Bordenave, Charles, Collins, Benoit
We consider a non-commutative polynomial in several independent $N$-dimensional random unitary matrices, uniformly distributed over the unitary, orthogonal or symmetric groups, and assume that the coefficients are $n$-dimensional matrices. The main p
Externí odkaz:
http://arxiv.org/abs/2304.05714
L\'evy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an $\alpha$-stable law. For $\alpha < 1$, predictions from the physics literature suggest that high-dimensional L\'{e}vy matrices should displa
Externí odkaz:
http://arxiv.org/abs/2210.09458
Autor:
Bordenave, Charles, Lee, Jaehun
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let $v$ be the top eigenvector of an $N\times N$ sparse random symmetric matrix with an average of $d$ non-zero centered entries per row. We resample $k$
Externí odkaz:
http://arxiv.org/abs/2106.09570
Autor:
Arras, Adam, Bordenave, Charles
We establish a quantitative criterion for an operator defined on a Galton-Watson random tree for having an absolutely continuous spectrum. For the adjacency operator, this criterion requires that the offspring distribution has a relative variance bel
Externí odkaz:
http://arxiv.org/abs/2105.10177
Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called "typical"
Externí odkaz:
http://arxiv.org/abs/2102.02653
Autor:
Bordenave, Charles, Collins, Benoit
Publikováno v:
Invent. Math. 237 (2024), no. 1, 221--273
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random permutations act
Externí odkaz:
http://arxiv.org/abs/2012.08759
Publikováno v:
Probab. Theory Related Fields 182 (2022), no. 3-4, 1163-1181
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in probability
Externí odkaz:
http://arxiv.org/abs/2012.05602