Related papers: Asymptotic behaviors of convolution powers of the …
We consider the zeta distributions which are discrete power law distributions that can be interpreted as the counterparts of the continuous Pareto distributions with unit scale. The family of zeta distributions forms a discrete exponential…
Expressing Weierstrass type infinite products in terms of Stieltjes integrals is discussed. The asymptotic behavior of particular types of infinite products is compared against the asymptotic behavior of the entire function Xi(s),…
We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.
Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice…
In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived…
We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations…
Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability distribution, and study in depth some asymptotic properties…
We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
We establish an unconditional asymptotic formula describing the horizontal distribution of the zeros of the derivative of the Riemann zeta-function. For $\Re(s)=\sigma$ satisfying $(\log T)^{-1/3+\epsilon} \leq (2\sigma-1) \leq (\log \log…
We study a discrete analogue of the classical multivariate Gaussian distribution. It is supported on the integer lattice and is parametrized by the Riemann theta function. Over the reals, the discrete Gaussian is characterized by the…
Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include…
We establish the unimodality and the asymptotic strong unimodality of the ordinary multinomials and give their smallest mode leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. We…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
For the Riemann zeta-function, we introduce a function such that it is a characteristic function of an infinitely divisible distribution on the real line if and only if the Riemann Hypothesis is true.