Related papers: Central Limit Theorems for Wavelet Packet Decompos…
In the averaging process on a graph $G = (V, E)$, a random mass distribution $\eta$ on $V$ is repeatedly updated via transformations of the form $\eta_{v}, \eta_{w} \mapsto (\eta_{v} + \eta_{w})/2$, with updates made according to…
Consider a homogeneous Poisson point process in a compact convex set in $d$-dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point…
We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998)…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
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 establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
Suppose $X = (X_x, x$ in $Z^d)$ is a family of i.i.d. variables in some measurable space, $B_0$ is a bounded set in $R^d$, and for $t > 1$, $H_t$ is a measure on $tB_0$ determined by the restriction of $X$ to lattice sites in or adjacent to…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
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…
The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…
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,…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
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…
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…
This paper deals with the union set of a stationary Poisson process of cylinders in $\mathbb{R}^n$ having an $(n-m)$-dimensional base and an $m$-dimensional direction space, where $m\in\{0,1,\ldots,n-1\}$ and $n\geq 2$. The concept…
We consider stochastic wave equations in spatial dimensions $d \geq 4$. We assume that the driving noise is given by a Gaussian noise that is white in time and has some spatial correlation. When the spatial correlation is given by the Riesz…
We find a sufficient condition under which a central limit theorem for a stationary linear process is quenched. We find a stationary linear process szatisfying the Maxwell-Woodroofe condition for which the variances of partial sums are…