---
_id: '181'
abstract:
- lang: eng
  text: 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.
acknowledgement: The work of the second author was also partially supported by the
  Hausdorff Center of Mathematics.
article_processing_charge: No
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
- first_name: David T
  full_name: Renfrew, David T
  id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
  last_name: Renfrew
  orcid: 0000-0003-3493-121X
citation:
  ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled
    differential equations. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(3):3271-3290.
    doi:<a href="https://doi.org/10.1137/17M1143125">10.1137/17M1143125</a>
  apa: Erdös, L., Krüger, T. H., &#38; Renfrew, D. T. (2018). Power law decay for
    systems of randomly coupled differential equations. <i>SIAM Journal on Mathematical
    Analysis</i>. Society for Industrial and Applied Mathematics . <a href="https://doi.org/10.1137/17M1143125">https://doi.org/10.1137/17M1143125</a>
  chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for
    Systems of Randomly Coupled Differential Equations.” <i>SIAM Journal on Mathematical
    Analysis</i>. Society for Industrial and Applied Mathematics , 2018. <a href="https://doi.org/10.1137/17M1143125">https://doi.org/10.1137/17M1143125</a>.
  ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of
    randomly coupled differential equations,” <i>SIAM Journal on Mathematical Analysis</i>,
    vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290,
    2018.
  ista: Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly
    coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3),
    3271–3290.
  mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential
    Equations.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3, Society
    for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:<a href="https://doi.org/10.1137/17M1143125">10.1137/17M1143125</a>.
  short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis
    50 (2018) 3271–3290.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-15T12:05:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/17M1143125
ec_funded: 1
external_id:
  arxiv:
  - '1708.01546'
  isi:
  - '000437018500032'
intvolume: '        50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1708.01546
month: '01'
oa: 1
oa_version: Published Version
page: 3271 - 3290
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 258F40A4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: M02080
  name: Structured Non-Hermitian Random Matrices
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7740'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Power law decay for systems of randomly coupled differential equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...