Related papers: q-Gaussian distributions. Simplifications and simu…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
We study the regularity of the law of a quadratic form $Q(X,X)$, evaluated in a sequence $X = (X_{i})$ of independent and identically distributed random variables, when $X_{1}$ can be expressed as a sufficiently smooth function of a…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical…
We present a trivial probabilistic illustration for representation of quantum mechanics as an algorithm for approximative calculation of averages.
We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta,…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…
Husimi distributions and Wigner distributions are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
Let $T$ be a random field invariant under the action of a compact group $G$. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that…