Related papers: On Conditioning Brownian Particles to Coalesce
We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…
The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian…
The purpose of this note is to give an example of stochastic flows of kernels, which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We study a model of mass-bearing coagulating planar Brownian particles. Coagulation is prone to occur when two particles become within a distance of order $\epsilon$. We assume that the initial number of particles is of the order of $| \log…
Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the…
Using Brownian dynamics computer simulations we show that a two-dimensional suspension of self-propelled ("active") colloidal particles crystallizes at sufficiently high densities. Compared to the equilibrium freezing of passive particles…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the…
Consider a finite system of Brownian particles on the real line. Each particle has drift and diffusion coefficients depending on its current rank relative to other particles, as in Karatzas, Pal and Shkolnikov (2012). We prove some…
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motions and create offspring at a constant rate. Particles of…
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise.…
Non-typical transport phenomena may arise when randomly driven particles remain in an active relationship with the environment instead of being passive. If we attribute to Brownian particles an ability to induce alterations of the…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…
We consider Galton-Watson trees associated with a critical offspring distribution and conditioned to have exactly $n$ vertices. These trees are embedded in the real line by affecting spatial positions to the vertices, in such a way that the…
We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate \beta > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles…