88 citations · 559 across the 17 of their papers we have counts for
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The continuous Anderson hamiltonian in dimension two
Romain Allez, Khalil Chouk
We define the Anderson hamiltonian on the two dimensional torus . This operator is formally defined as where is the Laplacian oper…
The eigenvectors of Gaussian matrices with an external source
Romain Allez, Joël Bun, Jean-Philippe Bouchaud
We consider a diffusive matrix process defined as where is a given deterministic Hermitian matrix and is a Hermitian Brownian mot…
From Sine kernel to Poisson statistics
Romain Allez, Laure Dumaz
We study the Sine process introduced in [B. Valkó and B. Virág. Invent. math. (2009)] when the inverse temperature tends to 0. This point process has been shown to be the s…
Random matrices in non-confining potentials
Romain Allez, Laure Dumaz
We consider invariant matrix processes diffusing in non-confining cubic potentials of the form . We construct the trajectories of such process…
Tracy-Widom at high temperature
Romain Allez, Laure Dumaz
We investigate the marginal distribution of the bottom eigenvalues of the stochastic Airy operator when the inverse temperature tends to . We prove that the minimal eigenval…
Index Distribution of the Ginibre Ensemble
Romain Allez, Jonathan Touboul, Gilles Wainrib
Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing…
Eigenvector dynamics under free addition
Romain Allez, Jean-Philippe Bouchaud
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…
A diffusive matrix model for invariant -ensembles
Romain Allez, Alice Guionnet
We define a new diffusive matrix model converging towards the -Dyson Brownian motion for all that provides an explicit construction of -ensembles of random matri…
Invariant -ensembles and the Gauss-Wigner crossover
Romain Allez, Jean-Philippe Bouchaud, Alice Guionnet
We define a new diffusive matrix model converging towards the -Dyson Brownian motion for all that provides an explicit construction of -ensembles of random matr…
Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure
Romain Allez, Rémi Rhodes, Vincent Vargas
We study the asymptotic of the spectral distribution for large empirical covariance matrices composed of independent Multifractal Random Walk processes. The asymptotic is taken as…
Lognormal scale invariant random measures
Romain Allez, Rémi Rhodes, Vincent Vargas
In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of…