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We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$started from step initial data and obtain the exact Lyapunov exponents for$H_0(t)$, the integrated current of ASEP. As a corollary, we derive an explicitformula for the upper-tail large deviation rate function for $-H_0(t)$. Ourresult matches with the rate function for the integrated current of the totallyasymmetric simple exclusion process (TASEP) obtained in [Johansson00](arXiv:math/9903134).

Upper-tail large deviation principle for the ASEP