November 25, 2021 @ Bâtiment IMAG (206) -- Seminar "Positive solutions for large random linear systems - application to theoretical ecology" by Jamal Najim
Large Lotka-Volterra (LV) systems of coupled differential equations is a popular model to describe the dynamics and equilibrium of the abundances of large populations in interaction such as foodwebs for instance. For such large LV systems, calibrating the interaction coefficients between the coupled equations is a highly difficult task that people often circumvent by considering instead random coefficients.
In this talk, we will describe feasible equilibria for such systems. By feasible equilibrium, we mean an equilibrium with no vanishing species. The study of such an equilibrium amounts to finding a positive solution to a simple large linear equation involving a large random matrix. We will describe solutions for various models: fully random (i.i.d.), sparse, correlated.
Key words are: Theoretical ecology, random Matrix Theory, concentration of measure, extreme values. Reference: arXiv:1904.04559
Joint work with I. Akjouj, P. Bizeul, M. Clénet, H. El Ferchichi.