Related papers: Clustering of large deviations in moving average p…
The influence of clustering on the collision rate of inertial particles in a smooth random velocity field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the the ratio between the relaxation time of the…
We present a Bayesian approach to predict the clustering of opinions for a system of interacting agents from partial observations. The Bayesian formulation overcomes the unobservability of the system and quantifies the uncertainty in the…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations…
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…
The probability distribution of the maximum $M_t$ of a single resetting Brownian motion (RBM) of duration $t$ and resetting rate $r$, properly centred and scaled, is known to converge to the standard Gumbel distribution of the classical…
We consider a cluster growth model on Z^d, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It…
A blocks method is used to define clusters of extreme values in stationary time series. The cluster starts at the first large value in the block and ends at the last one. The block cluster measure (the point measure at clusters) encodes…
We study the aggregation/disaggregation problem of random parameter AR(1) processes and its relation to the long memory phenomenon. We give a characterization of a subclass of aggregated processes which can be obtained from simpler,…
The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate…
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…
A review is given on the studies of formation of light clusters and heavier fragments in heavy-ion collisions at incident energies from several tens of MeV/nucleon to several hundred MeV/nucleon, focusing on dynamical aspects and on…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise. As the extreme events display large deviation from the mean behaviour, the noise…
We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the…
We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in…