Abstract
We consider the asymmetric simple exclusion process (ASEP) on started from step initial data and obtain the exact Lyapunov exponents for , the integrated current of ASEP. As a corollary, we derive an explicit formula for the upper-tail large deviation rate function for . Our result matches with the rate function for the integrated current of the totally asymmetric simple exclusion process (TASEP) obtained in [40].
Funding Statement
The authors were partially supported by Ivan Corwin’s NSF grant DMS:1811143 as well as the Fernholz Foundation’s “Summer Minerva Fellows” program.
Acknowledgments
We are grateful to Ivan Corwin for suggesting this problem and providing numerous stimulating discussions. His encouragement and inputs on earlier drafts of the paper have been invaluable. We also thank Evgeni Dimitrov, Li-Cheng Tsai, Yier Lin and Mark Rychnovsky for helpful conversations and Pierre Le Doussal and Alexandre Krajenbrink for providing many valuable references to the physics literature. Finally, we thank the anonymous referees for their careful reading and helpful suggestions for improvements.
Citation
Sayan Das. Weitao Zhu. "Upper-tail large deviation principle for the ASEP." Electron. J. Probab. 27 1 - 34, 2022. https://doi.org/10.1214/21-EJP730
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