Related papers: Random matrix theory within superstatistics
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
We show that the random matrix theory with non-integer "symmetry parameter" beta describes the statistics of transport parameters of strongly disordered two dimensional systems.
In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model…