Space-Time Current Process for Independent Random Walks in One Dimension

Details Space-Time Current Process for Independent Random Walks in One Dimension Space-Time Current Process for Independent Random Walks in One Dimension

2008-07-21

arxiv.org/abs/0807.3313v2

ALEA Lat. Am. J. Probab. Math. Stat. 4 (2008), 307 -- 336

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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.

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