Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions

DOI10.1016/j.spa.2022.08.004zbMath1503.37064arXiv2205.15591OpenAlexW4281691570MaRDI QIDQ2080292

Hafedh El Ferchichi, Maxime Clenet, Jamal Najim

Publication date: 7 October 2022

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.15591

zbMATH Keywords

linear systemsLotka-Volterra equationslarge random matricesGaussian concentration

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Population dynamics (general) (92D25) Ecology (92D40) Random matrices (algebraic aspects) (15B52) Generation, random and stochastic difference and differential equations (37H10)

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Uses Software

• GitHub

Cites Work

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• Global asymptotic stability in Volterra's population systems
• Qualitative behavior of \(n\)-dimensional ratio-dependent predator-prey systems
• The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations
• Spectral analysis of large dimensional random matrices
• Local elliptic law
• Low rank perturbations of large elliptic random matrices
• The Elliptic Law
• Elliptic Law
• Gaussian Hilbert Spaces
• Evolutionary Games and Population Dynamics
• Some estimates of norms of random matrices
• The Elliptic Law: ten years later I
• Positive solutions for large random linear systems