Related papers: Functional central limit theorem for subgraph coun…

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as…

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…

This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general…

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and…

The main result of this paper is a functional limit theorem for the sine-process. In particular, we study the limit distribution, in the space of trajectories, for the number of particles in a growing interval. The sine-process has the…

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…

For a $d\times d$ expanding matrix $A$, we investigate randomness of the sequence $\{A^k x\}$ and prove the central limit theorem for $\sum f(A^k x)$ where $f$ is a periodic function with a mild regularity condition.

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…

In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach…

In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…

This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…

We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a 2d-random walk in different situations: when the r.f. is iid with a second order moment (random sceneries), or when it is…

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…

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…

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…