Power law decay for systems of randomly coupled differential equations Journal Article


Author(s): Erdős, László; Krüger, Torben; Renfrew, David
Article Title: Power law decay for systems of randomly coupled differential equations
Affiliation IST Austria
Abstract: We consider large random matrices X with centered, independent entries but possibly di erent 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 di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.
Keywords: Random matrix; Differential equations; Power law decay; Autocorrelation function; Non-Hermitian random matrix; Time evolution of neural networks; Autocorrelation functions; G function; Large random matrices; Long-time asymptotics; Randomly coupled; Time evolutions; Autocorrelation
Journal Title: SIAM Journal on Mathematical Analysis
Volume: 50
Issue 3
ISSN: 00361410
Publisher: Society for Industrial and Applied Mathematics  
Date Published: 2018-01-01
Start Page: 3271
End Page: 3290
URL:
DOI: 10.1137/17M1143125
Open access: yes (repository)
IST Austria Authors
  1. László Erdős
    110 Erdős
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