Related papers: On generating functions of Hausdorff moment sequen…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…
In this paper we consider power and trigonometric series whose coefficients are supposed to satisfy the Hausdorff conditions, which play a relevant role in the moment problem theory. We prove that these series converge to functions analytic…
We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set $A$ whose indicator function is 'approximately multiplicative' and uniformly distributed on short…
We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and…
We consider a uniform distribution on the set $\mathcal{M}_k$ of moments of order $k \in \mathbb{N}$ corresponding to probability measures on the interval $[0,1]$. To each (random) vector of moments in $\mathcal{M}_{2n-1}$ we consider the…
We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towards (dis)proving a conjecture of Helson. We also prove…
We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words of length N from an alphabet of k letters. We find Toeplitz determinant representations for the exponential…
Let $(X,{\mathcal A},\mu)$ be a probability space and let $S\colon X\to X$ be a measurable transformation. Motivated by the paper of K. Nikodem [Czechoslovak Math. J. 41(116) (4) (1991) 565--569], we concentrate on a functional equation…
We investigate the moments of a smooth counting function of the zeros near the central point of L-functions of weight k cuspidal newforms of prime level N. We split by the sign of the functional equations and show that for test functions…
We establish the exact-order estimates of uniform approximations by the Zygmund sums $Z^{s}_{n-1}$ of $2\pi$-periodic continuous functions $f$ from the classes $C^{\psi}_{\beta,p}$.These classes are defined by the convolutions of functions…
In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed.…
In this paper we study the generating functionals of several random packing processes: the classical Mat\'ern hard-core model; its extensions, the $k$-Mat\'ern models and the $\infty$-Mat\'ern model, which is an example of random sequential…
We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional…
We introduce two families of generators (functions) $\mathcal{G}$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results…
This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables.…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial $Y = 1 + \xi_1 + \xi_1 \xi_2 + \xi_1 \xi_2 \xi_3 + ...$ of independent and identically distributed non-negative random variables. It…
The main result of the paper is the following. Let a non-degenerate distribution have finite moments $\mu_k$ of all orders $k=0,1,2,\ldots$. Then the sequence $\{\mu_k/k!, \; k=0,1,2,\ldots\}$ either contains infinitely many different terms…
We completely characterize the unimodal category for functions $f:\mathbb R\to[0,\infty)$ using a decomposition theorem obtained by generalizing the sweeping algorithm of Baryshnikov and Ghrist. We also give a characterization of the…