Related papers: A central limit theorem for the degree of a random…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\mu$a such that, for any…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.

We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…

The theory of products of random matrices and Lyapunov exponents have been widely studied and applied in the fields of biology, dynamical systems, economics, engineering and statistical physics. We consider the product of an i.i.d. sequence…

There is a well understood way of generating random coverings of a fixed manifold by sampling homomorphisms from the fundamental group of this manifold into the symmetric group. We prove a central limit theorem for the number of connected…

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…

We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…

We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space.

We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.

We study the limiting distribution of a volatility target index as the discretisation time step converges to zero. Two limit theorems (a strong law of large numbers and a central limit theorem) are established, and as an application, the…

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…

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…

In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc) of the asymptotic laws and of convergence rates were studied. However, for basically all…

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the…

In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We use Stein's method and the asymptotic lower bound for the variance of the area…