Related papers: q-Gaussian distributions. Simplifications and simu…
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…
In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We develop a simple algorithm to generate random variables described by densities equaling squared Hermite functions. As an application, we show how to generate a randomly chosen eigenvalue of a matrix from the Gaussian Unitary Ensemble…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…
We show that whenever data are gathered using a device that performs a normalization-preprocessing, the ensuing normalized input, as recorded by the measurement device, will always be q-Gaussian distributed if the incoming data exhibit…
Statistics over the Gaussian unitary ensemble and the Wishart ensemble of random matrices often have nice closed-form expressions. These are related to multivariate extensions of the Hermite, Laguerre, and Jacobi polynomials, which often…
The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize…
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is…
The eigenvalue probability density function of the Gaussian unitary ensemble permits a $q$-extension related to the discrete $q$-Hermite weight and corresponding $q$-orthogonal polynomials. A combinatorial counting method is used to specify…
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares.…
These lectures provide an informal introduction into the notions and tools used to analyze statistical properties of eigenvalues of large random Hermitian matrices. After developing the general machinery of orthogonal polynomial method, we…
We will prove that some weighted graphs on the distance $k$-graph of hypercubes approximate the $q$-Hermite polynomial of a $q$-gaussian variable by providing an appropriate matrix model.
We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…
A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time- (PT-) symmetric matrices. To illustrate the main idea, we first study 2*2…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…