Related papers: Functional Central Limit Theorem for Subgraph Coun…
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
In this paper we consider a dynamic Erd\H{o}s-R\'{e}nyi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this…
We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they…
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…
In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…
We study the fluctuations of subgraph counts in hyperbolic random geometric graphs on the $d$-dimensional Poincar\'e ball in the heterogeneous, heavy-tailed degree regime. In a hyperbolic random geometric graph whose vertices are given by a…
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,…
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…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
We consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. Every node has two states: it is either active or inactive. We assume that to each node is assigned a…
The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric complexes whose points lie in the tail of these noise distributions. This study advances…
We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…