Geodesic
Order of current variance and diffusivity in the asymmetric simple exclusion process
Márton Balázs1 ; Timo Seppäläinen2
1MTA-BME Stochastics Research Group<br/>Institute of Mathematics Budapest University of Technology and Economics<br/>1 Egry József u., 5th floor 7, Bld. H<br/>1111 Budapest<br/>Hungary
2Dept. of Mathematics<br/>419 Van Vleck Hall<br/>University of Wisconsin-Madison, Madison WI 53706-1388<br/>United States
Annals of mathematics, Tome 171 (2010) no. 2, pp. 1237-1265
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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.

DOI : 10.4007/annals.2010.171.1237

Márton Balázs   1   ; Timo Seppäläinen   2

1 MTA-BME Stochastics Research Group<br/>Institute of Mathematics Budapest University of Technology and Economics<br/>1 Egry József u., 5th floor 7, Bld. H<br/>1111 Budapest<br/>Hungary
2 Dept. of Mathematics<br/>419 Van Vleck Hall<br/>University of Wisconsin-Madison, Madison WI 53706-1388<br/>United States 
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Márton Balázs ; Timo Seppäläinen . Order of current variance and diffusivity in the asymmetric simple exclusion process. Annals of mathematics, Tome 171 (2010) no. 2, pp. 1237-1265. doi: 10.4007/annals.2010.171.1237

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