We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

A number of random matrix ensembles permitting exact determination of their eigenvalue
and eigenvector statistics maintain this property under a rank 1 perturbation. Considered in …

We consider a nonlinear autonomous system of N≫ 1 degrees of freedom randomly
coupled by both relaxational (“gradient”) and nonrelaxational (“solenoidal”) random …

We consider the generalized Lotka–Volterra system of equations with all-to-all, random
asymmetric interactions describing high-dimensional, very diverse and well-mixed …

We consider a simple neural network model, evolving via non-linear coupled stochastic
differential equations, where neural couplings are random Gaussian variables with non-zero …

In this chapter we review recent developments on the characterization of random
landscapes in high dimension. We focus in particular on the problem of characterizing the …

We consider a nonlinear autonomous random dynamical system of N degrees of freedom
coupled by Gaussian random interactions and characterized by a continuous spectrum n μ …

We review recent developments on the characterization of random landscapes in high-
dimension. We focus in particular on the problem of characterizing the landscape topology …

Consider a random matrix of size $ N $ as an additive deformation of the complex Ginibre
ensemble under a deterministic matrix $ X_0 $ with a finite rank, independent of $ N …

Understanding the conditions of feasibility and stability in ecological systems is a major
challenge in theoretical ecology. The seminal work of May in 1972 and recent developments …