Related papers: Pemantle's min-plus binary tree

In the recent trend of extending discrete-to-continuum limit passages for gradient flows of single-species particle systems with singular and nonlocal interactions to particles of opposite sign, any annihilation effect of particles with…

We numerically study structure and dynamics of single files composed of active particles, as well as, active-passive binary mixtures. Our simulation results show that when the persistent length of self-propelled particles is much larger…

We study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial…

Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…

Massive merging black holes will be the primary sources of powerful gravitational waves at low frequency, and will permit to test general relativity with candidate galaxies close to a binary black hole merger. In this paper we identify the…

We consider a system of annihilating particles where particles start from the points of a Poisson process on the line, move at constant i.i.d. speeds symmetrically distributed in {-1,0,+1} and annihilate upon collision. We prove that…

We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute…

The Marcus-Lushnikov process is a finite stochastic particle system, in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$. Under…

Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size $N$. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the…

We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root we prove that, in the limit as as…

Massive stars are known to have a high multiplicity, with examples of higher order multiples among the nearest and best studied objects. In this paper we study hierarchical multiple systems (an inner binary as a component of a wider binary)…

We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are…

In this short paper we discuss the possibility of testing the nature of astrophysical black holes using the recently observed black hole mergers. We investigate the possibility that a secondary black hole is created in the merger of two…

We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a…

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

Boson stars, self-gravitating objects made of a complex scalar field, have been proposed as simple models for very different scenarios, ranging from galaxy dark matter to black hole mimickers. Here we focus on a very compact type of boson…

Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…

We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…

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…

We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…