Related papers: Clustering of large deviations in moving average p…

We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…

We analyse large deviations of the magnetisation in two models of growing clusters. The models have symmetry-breaking transitions, so the typical magnetisation of a growing cluster may be either positive or negative, with equal probability.…

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from…

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is…

Many simple natural phenomena are characterized by complex motion that appears random at first glance, but that often displays underlying patterns and behavior that can be clustered in groups. The movement of small pieces of paper falling…

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been…

We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…

We study a simple aggregation model that mimics the clustering of traffic on a one-lane roadway. In this model, each ``car'' moves ballistically at its initial velocity until it overtakes the preceding car or cluster. After this encounter,…

Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…

We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…

We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse…

The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…

A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique…

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…

Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…

We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called…

A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously…

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation…

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling…

Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…