# Crowding of Brownian spheres

@article{Burdzy2010CrowdingOB, title={Crowding of Brownian spheres}, author={Krzysztof Burdzy and Soumik Pal and Jason Swanson}, journal={arXiv: Probability}, year={2010} }

We study two models consisting of reflecting one-dimensional Brownian "particles" of positive radius. We show that the stationary empirical distributions for the particle systems do not converge to the harmonic function for the generator of the individual particle process, unlike in the case when the particles are infinitely small.

## 4 Citations

### Archimedes' principle for Brownian liquid

- Physics, Mathematics
- 2009

We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary…

### Hydrodynamic Limit of a Boundary-Driven Elastic Exclusion Process and a Stefan Problem

- Mathematics
- 2011

Burdzy, Pal, and Swanson considered solid spheres of small radius moving in the unit interval, reflecting instantaneously from each other and at x=0, and killed at x=1, with mass being added to the…

### A Diffusive System Driven by a Battery or by a Smoothly Varying Field

- Mathematics
- 2010

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field…

### Conformal welding of uniform random trees

- Mathematics
- 2014

Conformal Welding of Uniform Random Trees Joel Barnes Chair of the Supervisory Committee: Professor Steffen Rohde Department of Mathematics A conformally balanced tree is an embedding of a given…

## References

SHOWING 1-10 OF 24 REFERENCES

### Positivity of the self-diffusion matrix of interacting Brownian particles with hard core

- Mathematics, Physics
- 1998

Abstract.We prove the positivity of the self-diffusion matrix of interacting Brownian particles with hard core when the dimension of the space is greater than or equal to 2. Here the self-diffusion…

### BROWNIAN PARTICLES WITH ELECTROSTATIC REPULSION ON THE CIRCLE: DYSON'S MODEL FOR UNITARY RANDOM MATRICES REVISITED

- Mathematics
- 2001

The Brownian motion model introduced by Dyson (7) for the eigenvalues of unitary random matrices N N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic…

### A system of infinitely many mutually reffecting Brownian balls in ℝd

- Mathematics
- 1996

SumamryAn infinite system of Skorohod type equations is studied. The unique solution of the system is obtained from a finite case by passing to the limit. It is a diffusion process describing a…

### Weak convergence of the scaled median of independent Brownian motions

- Mathematics
- 2007

AbstractWe consider the median of n independent Brownian motions, denoted by Mn(t), and show that
$$\sqrt{n}\,M_n$$ converges weakly to a centered Gaussian process. The chief difficulty is…

### Dirichlet form approach to infinite-dimensional Wiener processes with singular interactions

- Mathematics
- 1996

We construct infinite-dimensional Wiener processes with interactions by constructing specific quasi-regular Dirichlet forms. Our assumptions are very mild; accordingly, our results can be applied to…

### Diffusing particles with electrostatic repulsion

- Mathematics
- 1997

Summary.We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle…

### Asymptotics of particle trajectories in infinite one‐dimensional systems with collisions

- Mathematics
- 1985

We investigate the asymptotic behavior of the trajectories of a tagged particle (tp) in an infinite one-dimensional system of point particles. The particles move independently when not in contact:…

### A Brownian‐Motion Model for the Eigenvalues of a Random Matrix

- Physics
- 1962

A new type of Coulomb gas is defined, consisting of n point charges executing Brownian motions under the influence of their mutual electrostatic repulsions. It is proved that this gas gives an exact…

### Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction

- Mathematics
- 1977

The infinite system of Newton's equations of motion is considered for two-dimensional classical particles interacting by conservative two-body forces of finite range. Existence and uniqueness of…

### Diffusion with “collisions” between particles

- Mathematics, PhilosophyJournal of Applied Probability
- 1965

First consider two particles diffusing on the same line, with positions at time t given by y 1(t) and y2 (t) respectively. We suppose that they cannot pass one another, so that if initially y 1(0) <…