Related papers: A Central Limit Theorem and Exponential Correlatio…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
We investigate the effect of sequentiallydisrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two…
A self-consistent-field theory is given for the electronic collective modes of a chain containing a finite number, $N$, of Coulomb-coupled spherical two-dimensional electron gases (S2DE's) arranged with their centers along a straight line,…
We present results of a new model of sequential adsorption in which the adsorbing particles are correlated with the particles attached to the substrate. The strength of the correlations is measured by a tunable parameter $\sigma$. The model…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness. We show that for low values of the decay parameter the nodes with maximum decay…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
We consider random interlacements on $ \mathbb{Z}^d$, $d \ge 3$, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of…
We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…
The 't Hooft criterion leading to confinement out of a percolating cluster of central vortices suggests defining a novel three-dimensional gauge theory directly on a random percolation process. Wilson loop is viewed as a counter of…
We analyze a decomposition of the Coulomb electron-electron interaction into a long-range and a short-range part in the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study…
When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their size are important problems arising in statistics of…
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find…
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…
For one-dimensional many-body systems interacting via the \textit{Coulomb force} and with \textit{arbitrary} external potential energy, we derive (\textit{i}) the \textit{node coalescence condition} for the wave function. This condition…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…