Related papers: Cluster size distributions of discrete random fiel…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider…
We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents…
In a sample variance decomposition, with components functions of the sample's spacings, the largest component $\tilde{I}_n$ is used in cluster detection. It is shown for normal samples that the asymptotic distribution of $\tilde{I}_n$ is…
We report on the construction of a granular network of particles to study the formation, evolution and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically…
We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…
A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…
Recent empirical work [Leskovec2009] has suggested the existence of a size threshold for the existence of clusters within many real-world networks. We give the first proof that this clustering size threshold exists within a real-world…
We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is…
Max-stable random fields can be constructed according to Schlather (2002) with a random function or a stationary process and a kind of random event magnitude. These are applied for the modelling of natural hazards. We simply extend these…
We investigate the large-scale distribution of galaxy clusters taken from several X-ray catalogs. Different statistics of clustering like the conditional correlation function (CCF) and the minimal spanning tree (MST) as well as void…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
The probability distribution $\mu_{cl}$ of a general cluster point process in a Riemannian manifold $X$ (with independent random clusters attached to points of a configuration with distribution $\mu$) is studied via the projection of an…
Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…
The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
We use a sample of 53 galaxy clusters at 0.03 < z < 0.1 with available masses derived from the caustic technique and with velocity dispersions computed using 208 galaxies on average per cluster, in order to investigate the scaling between…
In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…
We consider stochastic lattice gases with stationary product weights and a polynomial perturbation vanishing with the system size that leads to condensation. If the density of particles exceeds a critical value the system phase separates…