For the 1D WASEP, the rescaled current and tagged particle satisfy sample path moderate deviation principles with speed a_n^2/n and explicit rate functions for β<1 and β>1.
Moderate deviation principles for the WASEP
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We study the weakly asymmetric simple exclusion process on the integer lattice. Under suitable constraints on the strength of the weak asymmetry of the dynamics, we prove moderate deviation principles for the fluctuation fields when the process starts from stationary measures. As an application, we obtain sample path moderate deviation principles for the occupation time of the process in one dimension.
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Moderate deviation principles for the current and the tagged particle in the WASEP
For the 1D WASEP, the rescaled current and tagged particle satisfy sample path moderate deviation principles with speed a_n^2/n and explicit rate functions for β<1 and β>1.