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

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.

to appear in Alea

References in corpus (2)

• On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion
• Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks

Cited by in corpus (7)

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• Current fluctuations of a system of one-dimensional random walks in random environment
• Hammersley's harness process: invariant distributions and height fluctuations
• Fluctuations of the empirical quantiles of independent Brownian motions
• An invariance principle for the stochastic heat equation
• Discrete Time Harness Processes
• Current fluctuations for independent random walks in multiple dimensions