## 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.

### MSC:

 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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