Related papers: Non-universality in clustered ballistic annihilati…
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 one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
We study universality classes and crossover behaviors in non-Abelian directed sandpile models, in terms of the metastable pattern analysis. The non-Abelian property induces spatially correlated metastable patterns, characterized by the…
We suggested a theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution. The reason of the {\em clustering instability} is a combined effect of the particle…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper,…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
A particle system is said to be non-exchangeable if two particles cannot be exchanged without modifying the overall dynamics. Because of this property, the classical mean-field approach fails to provide a limit equation when the number of…
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a…
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 perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic…
We consider a stochastic process that describes several particles interacting by either merging or annihilation. When two particles merge, they combine their masses; when annihilation occurs, only the particle of smallest mass survives.…
The Airy line ensemble is a random collection of continuous ordered paths that plays an important role within random matrix theory and the Kardar-Parisi-Zhang universality class. The aim of this paper is to prove a universality property of…
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of…
In overdamped particle motion across periodic landscapes, solitary cluster waves can occur at high particle densities and lead to particle transport even in the absence of thermal noise. Here we show that for driven motion under a constant…
A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for…