Related papers: A quenched CLT for super-Brownian motion with rand…
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…
The discounted central limit theorem concerns the convergence of an infinite discounted sum of i.i.d. random variables to normality as the discount factor approaches $1$. We show that, using the Fourier metric on probability distributions,…
We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the Central…
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>=2 of the fractional Brownian motion with Hurst parameter H in (0,1), where q is an integer. The central limit holds…
This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…
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…
We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy…
A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is…
We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on the universal cover of Riemannian manifolds of finite volume with pinched negative curvature. We further provide some…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson…
We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the…
Let $(Z_n)$ be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for $Z$ are investigated. Based on these results, the central limit theorem of $\log…
We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older…
We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…
We consider a nearest-neighbor, one-dimensional random walk $\{X_n\}_{n\geq 0}$ in a random i.i.d. environment, in the regime where the walk is transient with speed v_P > 0 and there exists an $s\in(1,2)$ such that the annealed law of…
We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…
Based on a combinatorial approach and random matrix theory, we show a central limit theorem that gives important insight into causally triangulated $3d$ quantum gravity.