Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks

• 成果类型: Article
• 署名作者: Seppäläinen, T
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000946
• 发表日期: 2005
• 页码: 759-797
• 关键词: simple exclusion process; continuum-limit; hydrodynamics

摘要

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.