Related papers: Central limit theorems for uniform model random po…
In this article, we investigate the asymptotic behavior of the solution to a one-dimensional stochastic heat equation with random nonlinear term generated by a stationary, ergodic random field. We extend the well-known central limit theorem…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and…
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…
In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…
Under the sublinear expectation $\mathbb{E}[\cdot]:=\sup_{\theta\in \Theta} E_\theta[\cdot]$ for a given set of linear expectations $\{E_\theta: \theta\in \Theta\}$, we establish a new law of large numbers and a new central limit theorem…
Fluctuations of the order parameters of the Gardner model for any $\alpha<\alpha_c$ are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.
We study cosmological polytopes induced by Erd\H{o}s--R\'enyi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…
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…
We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.
We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced in the paper "Limit velocity for a driven particle in a random medium with mass aggregation"…
We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…
We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…
We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…