Related papers: Strictly subgaussian probability distributions
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-dimensional sphere ($d\ge 2$). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for…
In testing the independence of two Gaussian populations, one computes the distribution of the sample canonical correlation coefficients, given that the actual correlation is zero. The "Laplace transform" of this distribution is not only an…
This work is devoted to a vast extension of Sanov's theorem, in Laplace principle form, based on alternatives to the classical convex dual pair of relative entropy and cumulant generating functional. The abstract results give rise to a…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
In these notes, we investigate the tail behaviour of the norm of subgaussian vectors in a Hilbert space. The subgaussian variance proxy is given as a trace class operator, allowing for a precise control of the moments along each dimension…
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…
The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian…
We study semiclassical sequences of distributions $u_h$ associated to a Lagrangian submanifold of phase space $\lag \subset T^*X$. If $u_h$ is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on $\lag,$ then the…
We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…
In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has…
We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a…
We prove Khinchin-type inequalities with sharp constants for type L random variables and all even moments. Our main tool is Hadamard's factorisation theorem from complex analysis, combined with Newton's inequalities for elementary symmetric…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
We prove tight bounds for the $\infty$-norm of the inverse of symmetric, diagonally dominant positive matrices. We also prove a new lower-bound form of Hadamard's inequality for the determinant of diagonally dominant positive matrices and…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…