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arXiv · 1708.01546

Power law decay for systems of randomly coupled differential equations

Laszlo Erdos·Torben Krüger·David Renfrew
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Abstract

We consider large random matrices $X$ with centered, independent entries but possibly different variances. We compute the normalized trace of $f(X) g(X^*)$ for $f,g$ functions analytic on the spectrum of $X$. We use these results to compute the long time asymptotics for systems of coupled differential equations with random coefficients. We show that when the coupling is critical the norm squared of the solution decays like $t^{-1/2}$.

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Laszlo Erdos, Torben Krüger, David Renfrew. 2017-08-04. Power law decay for systems of randomly coupled differential equations. https://doi.org/10.1137/17m1143125

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