Criticality in Brownian ensembles

Criticality in Brownian ensembles A Brownian ensemble appears as a nonequilibrium state of transition from one universality class of random matrix ensembles to another one. The parameter governing the transition is, in general, size-dependent, resulting in a rapid approach of the statistics, in infinite size limit, to one of the two universality classes. Our detailed analysis, however, reveals the appearance of a new scale-invariant spectral statistics, nonstationary along the spectrum, associated with multifractal eigenstates, and different from the two end-points if the transition parameter becomes size-independent. The number of such critical points during transition is governed by a competition between the average perturbation strength and the local spectral density. The results obtained here have applications to wide-ranging complex systems, e.g., those modeled by multiparametric Gaussian ensembles or column constrained ensembles. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Criticality in Brownian ensembles

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Criticality in Brownian ensembles

Abstract

A Brownian ensemble appears as a nonequilibrium state of transition from one universality class of random matrix ensembles to another one. The parameter governing the transition is, in general, size-dependent, resulting in a rapid approach of the statistics, in infinite size limit, to one of the two universality classes. Our detailed analysis, however, reveals the appearance of a new scale-invariant spectral statistics, nonstationary along the spectrum, associated with multifractal eigenstates, and different from the two end-points if the transition parameter becomes size-independent. The number of such critical points during transition is governed by a competition between the average perturbation strength and the local spectral density. The results obtained here have applications to wide-ranging complex systems, e.g., those modeled by multiparametric Gaussian ensembles or column constrained ensembles.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1539-3755
eISSN
550-2376
D.O.I.
10.1103/PhysRevE.96.012109
Publisher site
See Article on Publisher Site

Abstract

A Brownian ensemble appears as a nonequilibrium state of transition from one universality class of random matrix ensembles to another one. The parameter governing the transition is, in general, size-dependent, resulting in a rapid approach of the statistics, in infinite size limit, to one of the two universality classes. Our detailed analysis, however, reveals the appearance of a new scale-invariant spectral statistics, nonstationary along the spectrum, associated with multifractal eigenstates, and different from the two end-points if the transition parameter becomes size-independent. The number of such critical points during transition is governed by a competition between the average perturbation strength and the local spectral density. The results obtained here have applications to wide-ranging complex systems, e.g., those modeled by multiparametric Gaussian ensembles or column constrained ensembles.

Journal

Physical Review EAmerican Physical Society (APS)

Published: Jul 5, 2017

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