Introduction and guide to the handbook

Akemann, Gernot; Baik, Jinho; Francesco, P. Di

doi:10.1093/oxfordhb/9780198744191.013.1

Cited by 67 publications

(130 citation statements)

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“…RMT has numerous applications in many different fields, from condensed matter physics to financial markets ( e.g ., [ 51 ]). In the case of complex networks, the use of RMT techniques might reveal universal properties.…”

Section: Spectral Analysismentioning

confidence: 99%

Structural and spectral properties of generative models for synthetic multilayer air transportation networks

et al. 2021

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To understand airline transportation networks (ATN) systems we can effectively represent them as multilayer networks, where layers capture different airline companies, the nodes correspond to the airports and the edges to the routes between the airports. We focus our study on the importance of leveraging synthetic generative multilayer models to support the analysis of meaningful patterns in these routes, capturing an ATN’s evolution with an emphasis on measuring its resilience to random or targeted attacks and considering deliberate locations of airports. By resorting to the European ATN and the United States ATN as exemplary references, in this work, we provide a systematic analysis of major existing synthetic generation models for ATNs, specifically ANGEL, STARGEN and BINBALL. Besides a thorough study of the topological aspects of the ATNs created by the three models, our major contribution lays on an unprecedented investigation of their spectral characteristics based on Random Matrix Theory and on their resilience analysis based on both site and bond percolation approaches. Results have shown that ANGEL outperforms STARGEN and BINBALL to better capture the complexity of real-world ATNs by featuring the unique properties of building a multiplex ATN layer by layer and of replicating layers with point-to-point structures alongside hub-spoke formations.

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Section: Spectral Analysismentioning

confidence: 99%

Structural and spectral properties of generative models for synthetic multilayer air transportation networks

et al. 2021

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“…Random matrix theory (RMT) is an area of study in complex systems with a diverse range of applications [1][2][3]. This applicability largely owes to the generality of the question that RMT attempts to answer.…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue spectra and stability of directed complex networks

Baron

2022

Phys. Rev. E

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Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction network between components has on the eigenvalue spectrum. We build on previous results, which usually only take into account the mean degree of the network, by allowing for nontrivial network degree heterogeneity. We derive closed-form expressions for the eigenvalue spectrum of the adjacency matrix of a general weighted and directed network. Using these results, which are valid for any large well-connected complex network, we then derive compact formulas for the corrections (due to nonzero network heterogeneity) to well-known results in random matrix theory. Specifically, we derive modified versions of the Wigner semicircle law, the Girko circle law, and the elliptic law and any outlier eigenvalues. We also derive a surprisingly neat analytical expression for the eigenvalue density of a directed Barabási-Albert network. We are thus able to deduce that network heterogeneity is mostly a destabilizing influence in complex dynamical systems.

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“…One attraction of the random matrix approach is the ability to forgo solving microscopic scattering problems, provided that the appropriate probability distribution is known. The earliest random matrix models for the scattering matrix, namely the circular ensembles, use a uniform distribution over the unitary group [43]. A more sophisticated random matrix model is captured in the DMPK equation, which describes the statistical evolution of the singular values of the transmission matrix [44,45].…”

Section: Introductionmentioning

confidence: 99%

Random matrix theory of polarized light scattering in disordered media

Byrnes

Foreman

2022

Waves in Random and Complex Media

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In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering matrices automatically satisfy the physical constraints of unitarity, reciprocity and time reversal, whilst also incorporating the polarization properties of electromagnetic waves and scattering anisotropy. Our technique therefore enables statistical study of a variety of polarization phenomena, including depolarization rates and polarization-dependent scattering by chiral particles. In this vein, we perform numerical simulations for media containing isotropic and chiral spherical particles of different sizes for thicknesses ranging from the single to multiple scattering regime and discuss our results, drawing comparisons to established theory.

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Introduction and guide to the handbook

Cited by 67 publications

References 0 publications

Structural and spectral properties of generative models for synthetic multilayer air transportation networks

Structural and spectral properties of generative models for synthetic multilayer air transportation networks

Eigenvalue spectra and stability of directed complex networks

Random matrix theory of polarized light scattering in disordered media

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