Related papers: One-dimensional Brownian particle systems with ran…
We describe a two-dimensional model for active particles whose self-propulsion speed is not fixed, but varies in time, and whose motion is subject to both translational and rotational diffusion. In the conventional treatment of active…
Many studies on microscopic systems deal with Brownian particles embedded in media whose densities are different from that of the particles, causing them either to sink or float. The proximity to a wall modifies the friction force the…
Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary…
We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…
The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from everywhere in space and time, and the Brownian net is a generalization that also allows branching. They appear in the diffusive scaling limits of…
We study interacting Brownian particles on the half-line whose interaction occurs through boundary local times at the origin. The particle system is given by \[ X_i^n(t)=X^n_{0,i}+W_i^n(t)+L_i^n(t) +\frac{1}{n-1}\sum_{j\ne…
We computationally study suspensions of slow and fast active Brownian particles that have undergone motility induced phase separation and are at steady state. Such mixtures, of varying non-zero activity, remain largely unexplored even…
We develop a field theoretical treatment of a model of interacting Brownian particles. We pay particular attention to the requirement of the time reversal invariance and the fluctuation-dissipation relationship (FDR). The method used is a…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
The paper identifies families of quasi-stationary initial conditions for infinite Brownian particle systems within a large class and provides a construction of the particle systems themselves started from such initial conditions. Examples…
We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear…
We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
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…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
A theory for (1+3)-dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We derive the distribution of particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except…
$N$-Brownian bees is a branching-selection particle system in $\mathbb{R}^d$ in which $N$ particles behave as independent binary branching Brownian motions, and where at each branching event, we remove the particle furthest from the origin.…
In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases,…