Related papers: A strong law of large numbers for capacities
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
Consider the random polytope, that is given by the convex hull of a Poisson point process on a smooth convex body in $\mathbb{R}^d$. We prove central limit theorems for continuous motion invariant valuations including the Will's functional…
If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with…
We introduce a new class of real-valued monotones in preordered spaces, injective monotones. We show that the class of preorders for which they exist lies in between the class of preorders with strict monotones and preorders with countable…
We prove a local law in the bulk of the spectrum for random Gram matrices $XX^*$, a generalization of sample covariance matrices, where $X$ is a large matrix with independent, centered entries with arbitrary variances. The limiting…
We prove that the probability that a sum of independent random variables in $\mathbb{R}^d$ with bounded densities lies in a ball is maximized by taking uniform distributions on balls. This in turn generalizes a result by Rogozin on the…
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…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…
We show that the range of a critical branching random walk conditioned to survive forever and the Minkowski sum of two independent simple random walk ranges are intersection-equivalent in any dimension $d\ge 5$, in the sense that they hit…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) a sample is a measurable function from the index space, and (b) an idealization of the…
We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study…
We derive computational formulas for the generalized Choquet integral based on the novel survival function introduced by M. Boczek et al. [1]. We demonstrate its usefulness on the Knapsack problem and the problem of accommodation options.…
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…
We develop a probabilistic approach to study the volumetric and geometric properties of unit balls $\mathbb B_{q,1}^n$ of finite-dimensional Lorentz sequences spaces $\ell_{q,1}^n$. More precisely, we show that the empirical distribution of…
In this paper, we study voting rules on the interval domain, where the alternatives are arranged according to an externally given strict total order and voters report intervals of this order to indicate the alternatives they support. For…
We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…