Related papers: Deformed Gaussian Orthogonal Ensemble description …

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…

We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nested submatrices one obtains a limiting…

Using semiclassical periodic orbit theory for a chaotic system in a weak magnetic field, we obtain the form factor predicted by Pandey and Mehta's two matrix model up to the third order. The third order contribution has a peculiar term…

This paper presents a distributed algorithm on wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a linear size, lightweight, (1+\epsilon)-spanner for any given \epsilon > 0. A…

Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuations without performing any unfolding procedure. Here, SVD…

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…

In recent literature, the Gaussian Graphical model (GGM; Lauritzen, 1996),a network of partial correlation coefficients, has been used to capture potential dynamic relationships between observed variables. The GGM can be estimated using…

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…

We present a novel approach to study eigenvalues of deformed random matrices. This approach applies to many deformed Gaussian matrix models; two such models are studied in detail: the deformed GOE and the spiked population model.

Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…

Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is…

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i)…

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…

For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…

This is a collection of notes that are about spectral form factors of standard ensembles in the random matrix theory, written for the practical usage of current study of late time quantum chaos. More precisely, we consider Gaussian Unitary…

We study the spectral properties of and spectral-crossovers between different random matrix ensembles (Poissonian, GOE, GUE) in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term,…

Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…

Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…