Related papers: Limits of Probability Measures with General Coeffi…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain…
We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…
Multivariate Bessel processes describe the stochastic dynamics of interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and Laguerre ensembles. It was shown by Andraus, Katori, and Miyashita…
In this paper, we study Bessel processes of dimension $\delta\equiv2(1-\mu)$, with $0<\delta<2$, and some related martingales and random times. Our approach is based on martingale techniques and the general theory of stochastic processes…
Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
In this paper we show how to apply classical probabilistic tools for partial sums $\sum_{j=0}^{n-1}\varphi\circ\tau^j$ generated by a skew product $\tau$, built over a sufficiently well mixing base map and a random expanding dynamical…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\mu$a such that, for any…
The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…
We introduce the Plancherel measure on the set of partition collections, which parameterize irreducible representations of order n general linear group over a finite field. We prove that as n goes to infinity, the random partitions from the…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
One can consider $\mu$-Martin-L\"of randomness for a probability measure $\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters $p_0,…
In the spirit of the famous KOML\'OS (1967) theorem, every sequence of nonnegative, measurable functions $\{ f_n \}_{n \in \N}$ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in…
Which combinatorial sequences correspond to moments of probability measures on the real line? We present a generating function, in the form of a continued fraction, for a fourteen-parameter family of such sequences and interpret these in…