Power law decay for systems of randomly coupled differential equations

Laszlo Erdos; Torben Kruger; David Renfrew

doi:10.1137/17M1143125

Power law decay for systems of randomly coupled differential equations

Laszlo Erdos
, Torben Kruger
, David Renfrew

Mathematics and Statistics

Binghamton University

Institute of Science and Technology Austria

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	3271-3290
Number of pages	20
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	3
DOIs	https://doi.org/10.1137/17M1143125
State	Published - 2018

Keywords

Autocorrelation function
Non-Hermitian random matrix
Time evolution of neural networks

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title = "Power law decay for systems of randomly coupled differential equations",

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.",

keywords = "Autocorrelation function, Non-Hermitian random matrix, Time evolution of neural networks",

author = "Laszlo Erdos and Torben Kruger and David Renfrew",

note = "Publisher Copyright: {\textcopyright} 2018 SIAM.",

year = "2018",

doi = "10.1137/17M1143125",

language = "English",

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T1 - Power law decay for systems of randomly coupled differential equations

AU - Erdos, Laszlo

AU - Kruger, Torben

AU - Renfrew, David

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Autocorrelation function

KW - Non-Hermitian random matrix

KW - Time evolution of neural networks

UR - https://www.scopus.com/pages/publications/85049560155

U2 - 10.1137/17M1143125

DO - 10.1137/17M1143125

M3 - Article

SN - 0036-1410

VL - 50

SP - 3271

EP - 3290

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

Power law decay for systems of randomly coupled differential equations

Abstract

Keywords

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