Probability and Stochastic Analysis - University of Bonn
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Abstract of "Scaling limit for Brownian motions with one-sided collisions"

with Herbert Spohn and Thomas Weiss.

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 large time limit. This leads to a new universal cross-over process

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1502.01468