Zobrazeno 1 - 10
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pro vyhledávání: '"Allez, Romain"'
Autor:
Attal, Elie, Allez, Romain
We consider the eigenvectors of the principal minor of dimension $n< N$ of the Dyson Brownian motion in $\mathbb{R}^{N}$ and investigate their asymptotic overlaps with the eigenvectors of the full matrix in the limit of large dimension. We explicitly
Externí odkaz:
http://arxiv.org/abs/2409.17086
Autor:
Allez, Romain
Dans ce travail, nous nous sommes intéressés d'une part à la théorie du chaos multiplicatif Gaussien introduite par Kahane en 1985 et d'autre part à la théorie des matrices aléatoires dont les pionniers sont Wigner, Wishart et Dyson. La premi
Externí odkaz:
http://www.theses.fr/2012PA090046/document
Autor:
Allez, Romain, Chouk, Khalil
We define the Anderson hamiltonian on the two dimensional torus $\mathbb R^2/\mathbb Z^2$. This operator is formally defined as $\mathscr H:= -\Delta + \xi$ where $\Delta$ is the Laplacian operator and where $\xi$ belongs to a general class of singul
Externí odkaz:
http://arxiv.org/abs/1511.02718
We investigate the problem of estimating a given real symmetric signal matrix $\textbf{C}$ from a noisy observation matrix $\textbf{M}$ in the limit of large dimension. We consider the case where the noisy measurement $\textbf{M}$ comes either from a
Externí odkaz:
http://arxiv.org/abs/1502.06736
We consider a diffusive matrix process $(X_t)_{t\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the "external source" that one would like to es
Externí odkaz:
http://arxiv.org/abs/1412.7108
Autor:
Allez, Romain, Dumaz, Laure
Publikováno v:
Electron. J. Probab. 19 (2014) no. 114, 1-25
We study the Sine$_\beta$ process introduced in [B. Valk\'o and B. Vir\'ag. Invent. math. (2009)] when the inverse temperature $\beta$ tends to 0. This point process has been shown to be the scaling limit of the eigenvalues point process in the bulk
Externí odkaz:
http://arxiv.org/abs/1407.5402
Autor:
Allez, Romain, Dumaz, Laure
Publikováno v:
Journal of Statistical Physics August 2015, Volume 160, Issue 3, pp 681-714
We consider invariant matrix processes diffusing in non-confining cubic potentials of the form $V_a(x)= x^3/3 - a x, a\in \mathbb{R}$. We construct the trajectories of such processes for all time by restarting them whenever an explosion occurs, from
Externí odkaz:
http://arxiv.org/abs/1404.5265
Autor:
Allez, Romain, Dumaz, Laure
Publikováno v:
Journal of Statistical Physics, September 2014, Volume 156, Issue 6, pp 1146-1183
We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature $\beta$ tends to $0$. We prove that the minimal eigenvalue, whose fluctuations are governed by the Tracy-Widom $\beta$ law
Externí odkaz:
http://arxiv.org/abs/1312.1283
Publikováno v:
J. Phys. A: Math. Theor. 47 (2014) 042001
Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine estimates on the G
Externí odkaz:
http://arxiv.org/abs/1310.5039
Autor:
Allez, Romain, Bouchaud, Jean-Philippe
Publikováno v:
Random Matrices: Theory Appl. 03, 1450010 (2014)
We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble. We quantify the overlap between this single vector with the eigenvectors of the in
Externí odkaz:
http://arxiv.org/abs/1301.4939