Upper-tail large deviation principle for the ASEP

2021/04/01 by Sayan Das, Das, Sayan, Weitao Zhu +1 · 1 citation
Mathematics · Physics and Astronomy · #60F10 #82C22 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2104.00661

openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the asymmetric simple exclusion process (ASEP) on ℤ started from step initial data and obtain the exact Lyapunov exponents for H₀(t), the integrated current of ASEP. As a corollary, we derive an explicit formula for the upper-tail large deviation rate function for -H₀(t). Our result matches with the rate function for the integrated current of the totally asymmetric simple exclusion process (TASEP) obtained in [Johansson 00](arXiv:math/9903134).

Citations

• On the numerical evaluation of Fredholm determinants
• A Riemann-Hilbert approach to the lower tail of the KPZ equation

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• Precise large deviations in geometric last passage percolation

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