Related papers: Cepstral Analysis of Random Variables: Muculants
We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e. a point in the interior of the droplet where the density of the classical equilibrium measure…
We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
Fluctuations of observables provide unique insights into the nature of physical systems, and their study stands as a cornerstone of both theoretical and experimental science. Generalized fluctuations, or cumulants, provide information…
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for…
The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable. The key ingredient is a bound on cumulants of the type…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…