Related papers: Limit Theorems for Fr\'echet Mean Sets

The consistency of Fr\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies…

Strong laws of large numbers are established for random fields with weak or strong dependence. These limit theorems are applicable to random fields with heavy-tailed distributions including fractional stable random fields. The conditions…

Let f be a dominating meromorphic self-map of large topological degree on a compact Kaehler manifold. We give a new construction of the equilibrium measure of f and prove that it is exponentially mixing. Then, we deduce the central limit…

In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…

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…

TO BE PUBLISHED BY ISRAEL JOURNAL OF MATHEMATICS. We study the mean $\sum_{x\in\mathcal{X}} \bigl|\sum_{p\le N}{}u_p e(xp)\bigr|^{\ell}$ when $\ell$ covers the full range $[2,\infty)$ and $\mathcal{X}\subset\mathbb{R}/\mathbb{Z}$ is a…

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…

We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…

In his 1996 paper, Talagrand highlighted that the Law of Large Numbers (LLN) for independent random variables can be viewed as a geometric property of multidimensional product spaces. This phenomenon is known as the concentration of…

There is growing interest in developing statistical estimators that achieve exponential concentration around a population target even when the data distribution has heavier than exponential tails. More recent activity has focused on…

Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no…

Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…

Given a density t in (0,1], and a prime p, let S be any subset of F_p having at least tp elements, and having the least number of three-term arithmetic progressions mod p among all subsets of F_p with at least tp elements. Define N(t,p) to…

This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…

Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of…

Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems…

Let $X_1,\ldots,X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density $f$. Under some conditions on $f$, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability…

Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…

Let $1 < p < \infty$, $p\neq 2$. We prove that if $d\geq d_p$ is sufficiently large, and $A\subs\R^d$ is a measurable set of positive upper density then there exists $\la_0=\la_0(A)$ such for all $\la\geq\la_0$ there are $x,y\in\R^d$ such…