Related papers: A Moving Boundary Problem for Brownian Particles w…
Motivated by an approximation problem from mathematical finance, we analyse the stability of the boundary crossing probability for the multivariate Brownian motion process, with respect to small changes of the boundary. Under broad…
In this work, we focus on the behavior of a single passive Brownian particle in a suspension of passive particles with short-range repulsive interactions and a larger self-diffusion coefficient. While the forces affecting the…
We study a system of two reflected SPDEs which share a moving boundary. The equations describe competition at an interface and are motivated by the modelling of the limit order book in financial markets. The derivative of the moving…
The Brownian bees model is a branching particle system with spatial selection. It is a system of $N$ particles which move as independent Brownian motions in $\mathbb{R}^d$ and independently branch at rate 1, and, crucially, at each…
Brownian dynamics play a key role in understanding the diffusive transport of micro particles in a bounded environment. In geometries containing confining walls, physical laws determine the behavior of the random trajectories at the…
By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
We investigate the dynamics of Brownian particles in internal state- dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate…
We prove the convergence of $ \nN $-particle systems of Brownian particles with logarithmic interaction potentials onto a system described by the infinite-dimensional stochastic differential equation (ISDE). % For this proof we present two…
The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance the Brownian motion. In this paper we explore this duality for…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian…
We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a circular region with an absorbing boundary. Using the passive Brownian particle as basis states and dealing with the activity as a…
We show that for two classical brownian particles there exists an analog of continuous-variable quantum entanglement: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot be…
We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting…
Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. A triple…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a…
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…