On non-negative solutions to large systems of random linear equations

Stefan Landmann and Andreas Engel

Physica A: Statistical Mechanics and its Applications, 2020, vol. 552, issue C

Abstract: Systems of random linear equations may or may not have solutions with all components being non-negative. The question is, e.g., of relevance when the unknowns are concentrations or population sizes. In the present paper we show that if such systems are large the transition between these two possibilities occurs at a sharp value of the ratio between the number of unknowns and the number of equations. We analytically determine this threshold as a function of the statistical properties of the random parameters and show its agreement with numerical simulations. We also make contact with two special cases that have been studied before: the storage problem of a perceptron and the resource competition model of MacArthur.

Keywords: Disordered systems; Replica theory; Linear algebra (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119314554

DOI: 10.1016/j.physa.2019.122544

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