Related papers: Critical cluster cascades
In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…
We consider the Boolean model $Z$ on $\mathbb{R}^d$ with random compact grains, i.e. $Z := \bigcup_{i \in \mathbb{N}} (X_i + Z_i)$ where $\eta_t := \{X_1, X_2, \dots\}$ is a Poisson point process of intensity $t$ and $(Z_1, Z_2, \dots)$ is…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
We are interested in the survival probability of a population modeled by a critical branching process in an i.i.d. random environment. We assume that the random walk associated with the branching process is oscillating and satisfies a…
We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment…
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system…
We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We…
Sticks at one of different orientation are placed in an i.i.d. fashion at points of a Poisson point process of intensity $\lambda$. Sticks of the same direction have the same length, while sticks in different directions may have different…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
The article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster and then we apply the developed theory to determine the limiting…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We consider a supercritical general branching population where the lifetimes of individuals are i.i.d. with arbitrary distribution and each individual gives birth to new individuals at Poisson times independently from each others. The…
We consider biased random walks in a one-dimensional percolation model. This model goes back to Axelson-Fisk and H\"aggstr\"om and exhibits the same phase transition as biased random walk on the infinite cluster of supercritical Bernoulli…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…