Related papers: Cluster size distributions of discrete random fiel…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric…
We study a system of equal-sized circular discs each with an asymmetrically placed pivot at a fixed distance from the center. The pivots are fixed at the vertices of a regular triangular lattice. The discs can rotate freely about the…
We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…
The growth of a diffusion limited aggregation (DLA) cluster with mass $M$ and radius of gyration $R$ is described by a set of growth probabilities $\{ p_i\}$, where $p_i$ is the probability that the perimeter site $i$ will be the next to…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…
We compute the limiting distribution of height of a random discrete excursion with step sets consisting of one positive step 1 and arbitrary finite set of non-positive integers. The limit law is the supremum of a Brownian excursion. This is…
We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which…
Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption…
We consider a shot-noise field defined on a stationary determinantal point process on $\mathbb{R}^d$ associated with i.i.d. amplitudes and a bounded response function, for which we investigate the scaling limits as the intensity of the…
The problem of estimation of the distribution parameters on the sample when the part of these parameters are discrete (e.g. integer) is considered. We prove that the rate of convergence of MLE estimates under the natural conditions on the…
The main objective of this work is to study the existence of spatial patterns maximum annual rainfall (through daily observations) within the territory of Uruguay and to show the application of two new statistical tools recently proposed.…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles…
We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of…