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We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…

Chaotic Dynamics · Physics 2008-04-29 Eduardo G. Altmann , Tamas Tel

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the…

Statistical Finance · Quantitative Finance 2024-05-17 Samuel Forbes

Kaniadakis deformed \kappa-mathematics is an area of mathematics that has found relevance in the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay \kappa-differential equation is…

Mathematical Physics · Physics 2024-09-27 Rohan Bolle , Ibrahim Jarra , Jeffery A. Secrest

We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates $I$, where $N^\varepsilon \le | I | \le N^{1- \varepsilon}$, and prove it converges to a Gaussian at every energy level, including the edge,…

Probability · Mathematics 2023-05-16 Lucas Benigni , Patrick Lopatto

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…

Statistical Mechanics · Physics 2010-02-03 Jen-Hao Yeh , James A. Hart , Elliott Bradshaw , Thomas M. Antonsen , Edward Ott , Steven M. Anlage

The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [see U. Tirnakli, C. Beck and C. Tsallis, Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a q-Gaussian,…

Statistical Mechanics · Physics 2015-05-13 Ugur Tirnakli , Constantino Tsallis , Christian Beck

The generalized inverse Gaussian-Poisson (GIGP) distribution proposed by Sichel in the 1970s has proved to be a flexible fitting tool for diverse frequency data, collectively described using the item production model. In this paper, we…

Statistics Theory · Mathematics 2023-03-16 Leonid V. Bogachev , Ruheyan Nuermaimaiti , Jochen Voss

This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…

Mathematical Physics · Physics 2012-03-01 Fredy Zypman

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…

Statistical Mechanics · Physics 2007-05-23 A. Y. Abul-Magd

The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…

Chaotic Dynamics · Physics 2011-12-07 P. Leboeuf , A. G. Monastra

Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Abel Camacho

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de…

Probability · Mathematics 2013-08-20 Ivan Nourdin , Giovanni Peccati , Yvik Swan

We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…

Probability · Mathematics 2020-08-11 Yizhe Zhu

Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to…

Statistical Mechanics · Physics 2011-01-04 Massmimo Coraddu , Marcello Lissia , Roberto Tonelli

We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…

Mathematical Physics · Physics 2011-12-06 A. Abd El-Hady , A. Y. Abul-Magd

Let $\mathbf{X}\in\mathbb{C}^{n\times m}$ ($m\geq n$) be a random matrix with independent columns each distributed as complex multivariate Gaussian with zero mean and {\it single-spiked} covariance matrix $\mathbf{I}_n+ \eta…

Probability · Mathematics 2022-06-01 Pasan Dissanayake , Prathapasinghe Dharmawansa , Yang Chen

The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…

Quantum Physics · Physics 2022-05-03 Jonas Haferkamp , Christian Bertoni , Ingo Roth , Jens Eisert

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental…

High Energy Physics - Theory · Physics 2023-12-27 Felix M. Haehl , Wyatt Reeves , Moshe Rozali

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…

Disordered Systems and Neural Networks · Physics 2015-06-25 Michael Schreiber , Uwe Grimm , Rudolf A. Roemer , Jian-Xin Zhong