Mathematics – Probability
Scientific paper
2003-10-03
Annals of Probability 2005, Vol. 33, No. 2, 759-797
Mathematics
Probability
Published at http://dx.doi.org/10.1214/009117904000000946 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins
Scientific paper
10.1214/009117904000000946
Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n^{1/2} one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuations appear at scale n^{1/4} and converge to a certain self-similar Gaussian process. If the system is in equilibrium, this limiting process specializes to fractional Brownian motion with Hurst parameter 1/4. This contrasts with asymmetric exclusion and Hammersley's process whose second-order fluctuations appear at scale n^{1/3}, as has been discovered through related combinatorial growth models.
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