Related papers: Central limit theorems for a driven particle in a …
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…
Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any…
In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
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…
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…
We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function.…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem…
In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further…
We derive the radiation characteristics of an accelerated, charged particle in a model due to Caianiello in which the proper acceleration of a particle of mass $m$ has the upper limit $\mathcal{A}_m=2mc^3/\hbar$. We find two power laws, one…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.
Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
We prove a Central Limit Theorem for the finite dimensional distributions of the displacement for the 1D self-repelling diffusion which solves \begin{equation*} dX_t =dB_t -\big(G'(X_t)+ \int_0^t F'(X_t-X_s)ds\big)dt, \end{equation*} where…
For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…
In this paper we investigate a sequence of square integrable random processes with space varying memory. We establish sufficient conditions for the central limit theorem in the space $L^2(\mu)$ for the partial sums of the sequence of random…
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 prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result…