Summary
This paper is about the behavior of solutions to large systems of linear algebraic and differential equations when the coefficients are random variables. We will prove a law of large numbers and a central limit theorem for the solutions of certain algebraic systems, and the weak convergence to a Gaussian process for the solution of a system of differential equations. Some of the results were surprisingly difficult to prove, but they are all easily anticipated from a “chaos hypothesis”: i.e. an assumption of near independence for the components of the solutions of large systems of weakly coupled equations.
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Supported by the National Science Foundation under grant MCS76-80762, by the U.S. Air Force under grant AFOSR 78-3514 and the U.S. Army under grant DAAG 2980-K-0006
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Geman, S., Hwang, C.R. A chaos hypothesis for some large systems of random equations. Z. Wahrscheinlichkeitstheorie verw Gebiete 60, 291–314 (1982). https://doi.org/10.1007/BF00535717
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DOI: https://doi.org/10.1007/BF00535717