Approximate message passing for sparse matrices with application to the equilibria of large ecological Lotka-Volterra systems

DOI10.1016/j.spa.2023.104276arXiv2302.09847OpenAlexW4322715932MaRDI QIDQ6123262

Walid Hachem

Publication date: 4 March 2024

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

Full work available at URL: https://arxiv.org/abs/2302.09847

zbMATH Keywords

sparse random matricesapproximate message passingequilibria of ecological systemsLotka-Volterra ordinary differential equations

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Population dynamics (general) (92D25) Ecology (92D40) Random matrices (algebraic aspects) (15B52)

Cites Work

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• Sharp nonasymptotic bounds on the norm of random matrices with independent entries
• High dimensional robust M-estimation: asymptotic variance via approximate message passing
• An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model
• The spectral edge of some random band matrices
• Largest eigenvalues and eigenvectors of band or sparse random matrices
• Population dynamical behavior of Lotka-Volterra system under regime switching
• Shrinkage estimation
• Universality of approximate message passing algorithms
• Equilibrium in a large Lotka-Volterra system with pairwise correlated interactions
• Approximate message passing algorithms for rotationally invariant matrices
• Universality in polytope phase transitions and message passing algorithms
• Non-Negative Principal Component Analysis: Message Passing Algorithms and Sharp Asymptotics
• The Linear Complementarity Problem
• Perturbation Bounds of P-Matrix Linear Complementarity Problems
• State evolution for approximate message passing with non-separable functions
• State evolution for general approximate message passing algorithms, with applications to spatial coupling
• The Dynamics of Message Passing on Dense Graphs, with Applications to Compressed Sensing
• A Unifying Tutorial on Approximate Message Passing
• Optimal Transport