Universal hypotrochoidic law for random matrices with cyclic correlations

Aceituno, Pau Vilimelis and Rogers, Tim and Schomerus, Henning (2019) Universal hypotrochoidic law for random matrices with cyclic correlations. Physical Review E, 100 (1). ISSN 1539-3755

[img]
Text (paper_short_v15_PRE)
paper_short_v15_PRE.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (1MB)
[img]
Text (PhysRevE.100.010302_1_)
PhysRevE.100.010302_1_.pdf - Published Version
Available under License Unspecified.

Download (679kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Physical Review E
Additional Information:
© 2019 American Physical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100/3104
Subjects:
ID Code:
135483
Deposited By:
Deposited On:
17 Jul 2019 09:15
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Mar 2020 06:39