Brownian motion as limit of the interchange process

Mustazee Rahman, Balint Virag

Published 2016-09-25Version 1

We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on paths converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. Our approach provides a direct derivation of the hydrodynamic limit of the Simple Symmetric Exclusion process on paths.