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

Rohini Kumar

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arXiv · 0807.3313

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

Rohini Kumar

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Abstract

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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Rohini Kumar. 2008-10-21. Space-Time Current Process for Independent Random Walks in One Dimension. https://arxiv.org/abs/0807.3313

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