Brownian motion as limit of the interchange process
Probability
2017-02-03 v2
Abstract
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a law of large numbers type result for particle trajectories of the interchange process. After the completion of this manuscript we learned about a result of Durrett and Neuhauser that implies this result.
Keywords
Cite
@article{arxiv.1609.07745,
title = {Brownian motion as limit of the interchange process},
author = {Mustazee Rahman and Balint Virag},
journal= {arXiv preprint arXiv:1609.07745},
year = {2017}
}
Comments
Although this result is not new, Section 1.1 explains why we decided to keep the manuscript on the arxiv