Related papers: On Conditioning Brownian Particles to Coalesce
In this work, we obtain third order linear differential equation for stationary distributions of run-and-tumble particles in two-dimensions in a harmonic trap. The equation represents the condition $j = 0$ where $j$ is a flux and is…
In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the…
This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…
We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the…
An analog of the Trotter formula for the Arratia flow is presented. Perturbations of the Brownian web by mappings associated with an ordinary differential equation with a smooth right part are considered and proved to be convergent…
Within a simple model of attractive active Brownian particles, we predict flocking behavior and challenge the widespread idea that alignment interactions are necessary to observe this collective phenomenon. Here, we show that even…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
We propose discrete random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established…
We discuss the effect of an homogeneous flow in the aggregation process of colloidal magnetic particles at moderate concentration. Situations in which the presence of flow acts in favor of the chaining process: particles assemble into…
A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
Using a time-averaging technique we obtain exactly the probability distribution for position and velocity of a Brownian particle under the influence of two heat baths at different temperatures. These baths are expressed by a white noise…
The influence of an external field acting differently on the two constituents of a binary colloidal mixture performing Brownian dynamics is investigated by computer simulations and a simple theory. In our model, one half of the particles…
It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
The model consists of a signal process $X$ which is a general Brownian diffusion process and an observation process $Y$, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process $Y$ is…
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…