Related papers: Limit theory for geometric statistics of point pro…
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…
The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…
\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\{\mathcal{X}_{n}(i)$ $:$ $1$ $\leq $ $i$ $\leq $ $\mathcal{L}\}_{n\geq 1}$, where each $\mathcal{X}_{n}(i)$ is assumed to converge in…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…
Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model a static nonlinear susceptibility related to a four-point density correlation function, and show that it grows and…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…
A random geometric graph $G(\mathcal{X}_n, r_n)$ is formed by taking a binomial process $\mathcal{X}_n$ as the set of vertices and joining any two distinct points with an edge if they lie within distance $r_n$ of each other. We investigate…
We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…
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…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
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…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…
Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…