Related papers: Non-extensive Random Matrix Theory - A Bridge Conn…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
The model of heavy Wigner matrices generalizes the classical ensemble of Wigner matrices: the sub-diagonal entries are independent, identically distributed along to and out of the diagonal, and the moments its entries are of order 1/N,…
It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from…
In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are…
Properties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results. We present a slightly different view and…
Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace…
For certain families of finite quantum graphs, we study the question of how eigenfunctions are distributed over the graph. To characterize properties of the distribution, generalized entropies of the R\'{e}nyi and Tsallis types are…
We study random band matrices within the framework of traffic probability, an operadic non-commutative probability theory introduced by Male based on graph operations. As a starting point, we revisit the familiar case of the permutation…
We discuss the idea that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can…
A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…
In this paper, we are interested in sequences of q-tuple of N-by-N random matrices having a strong limiting distribution (i.e. given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its…