Related papers: Limit Theorems for Random Sums of Random Summands

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…

In recent years, tensors have been applied to different applications in science and engineering fields. In order to establish theory about tail bounds of the tensors summation behavior, this work extends previous work by considering the…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

The field of analytic combinatorics is dedicated to the creation of effective techniques to study the large-scale behaviour of combinatorial objects. Although classical results in analytic combinatorics are mainly concerned with univariate…

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…

We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…

We study sums of a random multiplicative function; this is an example, of number-theoretic interest, of sums of products of independent random variables (chaoses). Using martingale methods, we establish a normal approximation for the sum…

We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the "shapes" of datasets. The main focus of this paper is persistent homology, a ubiquitous tool in TDA. Basing our study on this, we…

We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random…

We prove a quantitative local limit theorem for the number of descents in a random permutation. Our proof uses a conditioning argument and is based on bounding the characteristic function $\phi(t)$ of the number of descents. We also…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…

In the framework of generalized Oppenheim expansions we prove strong law of large numbers for lightly trimmed sums. In the first part of this work we identify a particular class of expansions for which we provide a convergence result…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise…

We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…