2023/02/15 by Imane Akjouj, Akjouj, Imane, Walid Hachem +5 · 1 citation
Agricultural and Biological Sciences · Medicine · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Plant and animal studies #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2302.07820
openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix. Under some known conditions, a global equilibrium exists and is unique. In this article, we rigorously study its statistical properties in the large dimensional regime. Such an equilibrium vector is known to be the solution of a so-called Linear Complementarity Problem (LCP). We describe its statistical properties by designing an Approximate Message Passing (AMP) algorithm, a technique that has recently aroused an intense research effort in the fields of statistical physics, Machine Learning, or communication theory. Interaction matrices taken from the Gaussian Orthogonal Ensemble, or following a Wishart distribution are considered. Beyond these models, the AMP approach developed in this article has the potential to describe the statistical properties of equilibria associated to more involved interaction matrix models.