201 citations · 621 across the 50 of their papers we have counts for
55 papers
The SK model with a sparse variance profile: free energy and AMP algorithm for TAP equations at high temperature
Walid Hachem
A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular…
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…
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…
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…