Universität zu Köln

Saber, Sina and Saberi, Abbas Ali ORCID: 0000-0001-8864-4748 (2022). Universal scaling and criticality of extremes in random matrix theory. Phys. Rev. E, 105 (2). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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Abstract

We present a random matrix realization of a two-dimensional percolation model with the occupation probability p. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue resides on the moving edge of the semicircle bulk distribution with an additional semicircle functionality on p, the first extreme exhibits a disjoint isolated Gaussian statistics which is responsible for the emergence of a rich finite-size scaling and criticality. Our extensive numerical simulations along with analytical arguments unravel the power-law divergences due to the coalescence of the first two extreme eigenvalues in the thermodynamic limit. We develop a scaling law that provides a universal framework in terms of a set of scaling exponents uncovering the full finite-size scaling behavior of the extreme eigenvalue's fluctuation. Our study may provide a simple practical approach to capture the criticality in complex systems and their inverse problems with a possible extension to the interacting systems.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Saber, Sina UNSPECIFIED UNSPECIFIED UNSPECIFIED Saberi, Abbas Ali UNSPECIFIED orcid.org/0000-0001-8864-4748 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-664156
DOI:	10.1103/PhysRevE.105.L022102
Journal or Publication Title:	Phys. Rev. E
Volume:	105
Number:	2
Date:	2022
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2470-0053
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CHARACTERISTIC VECTORS; BORDERED MATRICES; DISTRIBUTIONS; TRANSITION Multiple languages Physics, Fluids & Plasmas; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66415