Kumar, Rohini Space-time current process for independent random walks in one dimension. (English) Zbl 1162.60345 ALEA, Lat. Am. J. Probab. Math. Stat. 4, 307-336 (2008). Summary: In a system made up of independent random walks, fluctuations of order \(n^{1/4}\) from the hydrodynamic limit come from particle current across characteristics. We show that a two-parameter space-time particle current process converges to a two-parameter Gaussian process. These Gaussian processes also appear as the limit for the one-dimensional random average process. The final section of this paper looks at large deviations of the current process. Cited in 6 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F10 Large deviations 60F17 Functional limit theorems; invariance principles 60G15 Gaussian processes Keywords:independent random walks; hydrodynamic limit; fluctuations; large deviation PDFBibTeX XMLCite \textit{R. Kumar}, ALEA, Lat. Am. J. Probab. Math. Stat. 4, 307--336 (2008; Zbl 1162.60345) Full Text: arXiv