Related papers: A centra-limit theorem for conservative fragmentat…

We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…

We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse…

In this article, we will consider Wishart Matrices with correlated entries, but with a strictly log-concave law. It has been shown by A.Pajor and L.Pastur that the empirical measures of such matrices converges. We will show, under some…

We give estimates on the rate of convergence in the Boolean central limit theorem for the L\'evy distance. In the case of measures with bounded support we obtain a sharp estimate by giving a qualitative description of this convergence.

We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…

In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval $[0;n]$ as $n\to\infty$ and obtain an estimate of the Berry-Esseen type for the rate of this…

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…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

Aims. Our goal is to find a converged cooling limit for fragmentation in self-gravitating disks. This is especially interesting for the formation of planets, brown dwarfs or stars and the growth of black holes. While investigating the…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

A famous result in renewal theory is the Central Limit Theorem for renewal processes. As in applications usually only observations from a finite time interval are available, a bound on the Kolmogorov distance to the normal distribution is…

We consider a class of interacting particle systems with values in $[0,\8)^{\zd}$, of which the binary contact path process is an example. For $d \ge 3$ and under a certain square integrability condition on the total number of the…

We prove central limit theorems for the number of descents and the number of inversions after a shelf-shuffle. In particular, we bound the convergence rate for the number of inversions independently of the number of shelves. Along the way,…

Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$…

We prove an upper bound for the convergence rate of the homogenization limit $\epsilon\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $\epsilon$ is a…

We explore statistical inference in self-similar conservative fragmentation chains when only approximate observations of the sizes of the fragments below a given threshold are available. This framework, introduced by Bertoin and Martinez…

In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to…

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…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

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…