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

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.

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      CODEN = {ANMAAH},
      MRCLASS = {60K35 (60J25 60J35)},
      MRNUMBER = {2005d:60156},
      MRREVIEWER = {Laurent Miclo},
      DOI = {10.4007/annals.2004.159.377},
      ZBLNUMBER = {1060.60099},
      }

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