Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n1/2 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 n1/4 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 n1/3, as has been discovered through related combinatorial growth models.
Publié le : 2005-03-14
Classification:
Independent random walks,
Hammersley’s process,
hydrodynamic limit,
fluctuations,
fractional Brownian motion,
60K35,
60F17
@article{1109868599,
author = {Sepp\"al\"ainen, Timo},
title = {Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 759-797},
language = {en},
url = {http://dml.mathdoc.fr/item/1109868599}
}
Seppäläinen, Timo. Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks. Ann. Probab., Tome 33 (2005) no. 1, pp. 759-797. http://gdmltest.u-ga.fr/item/1109868599/