Space-time current process for independent random walks in one dimension. (English) Zbl 1162.60345

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.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F10 Large deviations
60F17 Functional limit theorems; invariance principles
60G15 Gaussian processes
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