## Electronic Journal of Probability

### Brownian motions with one-sided collisions: the stationary case

#### Abstract

We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution we consider initial configurations distributed according to a Poisson point process with constant intensity, which makes the process space-time stationary. We prove convergence to the Airy process for stationary the case. As a byproduct we obtain a novel representation of the finite-dimensional distributions of this process. Our method differs from the one used for the TASEP and the KPZ equation by removing the initial step only after the limit $t\to\infty$. This leads to a new universal cross-over process.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 69, 41 pp.

Dates
Accepted: 23 June 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067175

Digital Object Identifier
doi:10.1214/EJP.v20-4177

Mathematical Reviews number (MathSciNet)
MR3361257

Zentralblatt MATH identifier
1327.60188

Subjects

Rights

#### Citation

Ferrari, Patrik; Spohn, Herbert; Weiss, Thomas. Brownian motions with one-sided collisions: the stationary case. Electron. J. Probab. 20 (2015), paper no. 69, 41 pp. doi:10.1214/EJP.v20-4177. https://projecteuclid.org/euclid.ejp/1465067175

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