Related papers: A simple rank-based Markov chain with self-organiz…
We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By…
In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the…
A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…
The Bak Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly…
We examine a discrete-time Markovian particle system on the quarter-plane introduced by M. Defosseux. The vertical boundary acts as a reflecting wall. The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall universality…
We introduce two sandpile models which show the same behavior of real sandpiles, that is, an almost self-organized critical behavior for small systems and the dominance of large avalanches as the system size increases. The systems become…
We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns…
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We consider a one-dimensional piecewise deterministic Markov process (PDMP) on $[0,1]$ with resetting at $0$ and depending on a small parameter $\varepsilon>0$. In the singular vanishing limit $\varepsilon \to 0$ we prove that the ``…
We study analytically the order and gap statistics of particles at time $t$ for the one dimensional branching Brownian motion, conditioned to have a fixed number of particles at $t$. The dynamics of the process proceeds in continuous time…
A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its…
We define a family of continuous-time branching particle systems on the non-negative real line, called branching subordinators, where particles move as independent subordinators. Each particle can also split (at possibly infinite rate) into…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites).…
In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves…
A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$, are observed sequentially by the grader.…