Order of current variance and diffusivity in the asymmetric simple exclusion process

Márton Balázs; Timo Seppäläinen

doi:http://doi.org/10.4007/annals.2010.171.1237

Pages 1237-1265 from Volume 171 (2010), Issue 2 by Márton Balázs , Timo Seppäläinen

Abstract

We prove that the variance of the current across a characteristic is of order $t^{2/3}$ in a stationary asymmetric simple exclusion process, and that the diffusivity has order $t^{1/3}$. The proof proceeds via couplings to show the corresponding moment bounds for a second class particle.

Milestones

Received: 18 August 2006
Revised: 29 January 2008
Accepted: 13 August 2008
Published online: 25 March 2010

Authors

Márton Balázs

MTA-BME Stochastics Research Group
Institute of Mathematics Budapest University of Technology and Economics
1 Egry József u., 5th floor 7, Bld. H
1111 Budapest
Hungary

Timo Seppäläinen

Dept. of Mathematics
419 Van Vleck Hall
University of Wisconsin-Madison, Madison WI 53706-1388
United States