Exceedingly large deviations of the totally asymmetric exclusion process

@article{Olla2019ExceedinglyLD,
  title={Exceedingly large deviations of the totally asymmetric exclusion process},
  author={Stefano Olla and Li-Cheng Tsai},
  journal={Electronic Journal of Probability},
  year={2019}
}
Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice $ \mathbb{Z} $. We study the functional Large Deviations of the integrated current $ \mathsf{h}(t,x) $ under the hyperbolic scaling of space and time by $ N $, i.e., $ \mathsf{h}_N(t,\xi) := \frac{1}{N}\mathsf{h}(Nt,N\xi) $. As hinted by the asymmetry in the upper- and lower-tail large deviations of the exponential Last Passage Percolation, the TASEP exhibits two types of deviations. One type of deviations… 
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