2003/10/31 by Timo Seppäläinen, Timo Seppalainen · 3 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F17. #msc:60K35
paper · pdf · doi:10.1214/009117904000000946
published as Annals of Probability 2005, Vol. 33, No. 2, 759-797 · Published at http://dx.doi.org/10.1214/009117904000000946 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/03/01 · arxiv created 2005/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.