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  • paper_short_v15_PRE

    Rights statement: © 2019 American Physical Society

    Accepted author manuscript, 1.12 MB, PDF document

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Universal hypotrochoidic law for random matrices with cyclic correlations

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Universal hypotrochoidic law for random matrices with cyclic correlations. / Aceituno, Pau Vilimelis; Rogers, Tim; Schomerus, Henning.
In: Physical Review E, Vol. 100, No. 1, 010302, 16.07.2019.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Aceituno, PV, Rogers, T & Schomerus, H 2019, 'Universal hypotrochoidic law for random matrices with cyclic correlations', Physical Review E, vol. 100, no. 1, 010302. https://doi.org/10.1103/PhysRevE.100.010302

APA

Aceituno, P. V., Rogers, T., & Schomerus, H. (2019). Universal hypotrochoidic law for random matrices with cyclic correlations. Physical Review E, 100(1), Article 010302. https://doi.org/10.1103/PhysRevE.100.010302

Vancouver

Aceituno PV, Rogers T, Schomerus H. Universal hypotrochoidic law for random matrices with cyclic correlations. Physical Review E. 2019 Jul 16;100(1):010302. doi: 10.1103/PhysRevE.100.010302

Author

Aceituno, Pau Vilimelis ; Rogers, Tim ; Schomerus, Henning. / Universal hypotrochoidic law for random matrices with cyclic correlations. In: Physical Review E. 2019 ; Vol. 100, No. 1.

Bibtex

@article{6c13edb58c5d445ca0dc4b43e2c2cd10,
title = "Universal hypotrochoidic law for random matrices with cyclic correlations",
abstract = "The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry. This hypotrochoid law applies to full matrices as well as sparse ones, and thereby holds with remarkable universality. We further extend our analysis to matrices and graphs with competing cycle motifs, which are described more generally by polytrochoid spectral boundaries.",
author = "Aceituno, {Pau Vilimelis} and Tim Rogers and Henning Schomerus",
note = "{\textcopyright} 2019 American Physical Society",
year = "2019",
month = jul,
day = "16",
doi = "10.1103/PhysRevE.100.010302",
language = "English",
volume = "100",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Universal hypotrochoidic law for random matrices with cyclic correlations

AU - Aceituno, Pau Vilimelis

AU - Rogers, Tim

AU - Schomerus, Henning

N1 - © 2019 American Physical Society

PY - 2019/7/16

Y1 - 2019/7/16

N2 - The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry. This hypotrochoid law applies to full matrices as well as sparse ones, and thereby holds with remarkable universality. We further extend our analysis to matrices and graphs with competing cycle motifs, which are described more generally by polytrochoid spectral boundaries.

AB - The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry. This hypotrochoid law applies to full matrices as well as sparse ones, and thereby holds with remarkable universality. We further extend our analysis to matrices and graphs with competing cycle motifs, which are described more generally by polytrochoid spectral boundaries.

U2 - 10.1103/PhysRevE.100.010302

DO - 10.1103/PhysRevE.100.010302

M3 - Journal article

VL - 100

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 010302

ER -