Universal hypotrochoidic law for random matrices with cyclic correlations

Pau Vilimelis Aceituno, Tim Rogers, Henning Schomerus

Research output: Contribution to journalArticlepeer-review

10 Citations (SciVal)


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.

Original languageEnglish
Article number010302
Pages (from-to)1-5
Number of pages5
JournalPhysical Review E
Issue number1
Publication statusPublished - 16 Jul 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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