Related papers: Correction. Central limit theorems for additive fu…

We correct a simple error in Percolation on random Johnson-Mehl tessellations and related models, Probability Theory and Related Fields 140 (2008), 417-468. (See also arXiv:math/0610716)

We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.

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…

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.

In this addendum we extend Theorem 4.6 on the negative binomial distribution in `Bounds for survival probabilities in supercritical Galton-Watson processes and applications to population genetics' (Journal of Mathematical Biology 92:40,…

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…

This note replies Dr. Jensen (2010) comments on Problem 2.3, which was left in Fuh (2010). In the following, we use the same notations and definitions in Fuh (2006) unless specified.

Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…

Correction to Bernoulli (2006), 12, 551--570 http://projecteuclid.org/euclid.bj/1151525136

It is demonstrated that the "generalized fluctuation-dissipation theorem" [Physica A 106, 443 (1981)] covers the later suggested "fluctuation theorems" and related statistical equalities.

We study the simplifications occurring in any likelihood function in the presence of a large number of small systematic uncertainties. We find that the marginalisation of these uncertainties can be done analytically by means of second-order…

An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for…

We consider a supercritical general branching population where the lifetimes of individuals are i.i.d. with arbitrary distribution and each individual gives birth to new individuals at Poisson times independently from each others. The…

We review recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The limit laws are expressed in terms of a certain Painlev\'e II function. Furthermore, we take this…

Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and consequently give the modified results.

We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…

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 paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the…

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.

We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…