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Approximate Message Passing for sparse matrices with application to the equilibria of large ecological Lotka-Volterra systems
Walid Hachem
This paper is divided into two parts. The first part is devoted to the study of a class of Approximate Message Passing (AMP) algorithms which are widely used in the fields of stati…
Extreme eigenvalues and eigenvectors for finite rank additive deformations of non-hermitian sparse random matrices
Walid Hachem, Michail Louvaris, Jamal Najim
Consider a sparse non-Hermitian random matrix defined as the Hadamard product between a random matrix with centered independent and identically distributed entrie…
Spin glass analysis of the invariant distribution of a Lotka-Volterra SDE with a large random interaction matrix
Mohammed Younes Gueddari, Walid Hachem
The generalized Lotka-Volterra stochastic differential equation with a symmetric food interaction matrix is frequently used to model the dynamics of the abundances of the species l…
On the spectral radius and the characteristic polynomial of a random matrix with independent elements and a variance profile
Walid Hachem, Michail Louvaris
In this paper, it is shown that with large probability, the spectral radius of a large non-Hermitian random matrix with a general variance profile does not exceed the square root o…
Long run convergence of discrete-time interacting particle systems of the McKean-Vlasov type
Pascal Bianchi, Walid Hachem, Victor Priser
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a…
Approximate Message Passing for general non-Symmetric random matrices
Mohammed-Younes Gueddari, Walid Hachem, Jamal Najim
Approximate Message Passing (AMP) algorithms are a family of iterative algorithms based on large random matrices with the special property of tracking the statistical properties of…