Related papers: Nonextensive random-matrix theory based on Kaniada…
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…
The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
New class of reference distribution functions for numerical approximation of the solution of the Fokker-Planck equations associated to the charged particle dynamics in tokamak are studied. The reference distribution functions are obtained…
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Traditionally, the Method of (Shannon-Kullback's) Relative Entropy Maximization (REM) is considered with linear moment constraints. In this work, the method is studied under frequency moment constraints which are non-linear in…
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…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of $3\times 3$ upper triangular matrices with real entries. We explore consequences of this embedding and of the…
In this paper non-asymptotic exact rearrangement invariant norm estimates are derived for the maximum distribution of the family elements of some rearrangement invariant (r.i.) space over unbounded measure in the entropy terms and in the…
We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…
We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in…
Tsallis entropy is a useful one-parameter generalization of the standard von Neumann entropy in information theory. We study the variance of Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
We show that some of the best-known matrix decompositions of some of the best-known random matrix ensembles give us the unique $G$-invariant uniform distributions on some of the best-known manifolds. The eigenvectors distributions of the…
The distributions of the spacing s between nearest-neighbor levels of unfolded spectra of random matrices from the beta-Hermite ensemble (beta-HE) is investigated by Monte Carlo simulations. The random matrices from the beta-HE are…
By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, R\'{e}nyi proposed the first formal generalization of Shannon entropy. Using…