January 2022 Hidden invariance of last passage percolation and directed polymers
Duncan Dauvergne
Author Affiliations +
Ann. Probab. 50(1): 18-60 (January 2022). DOI: 10.1214/21-AOP1527


Last passage percolation and directed polymer models on 2 are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK correspondence (e.g., geometric last passage percolation or the log-gamma polymer), we show that these basic invariances can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance statements for last passage times, geodesic locations, disjointness probabilities, polymer partition functions and quenched polymer measures. We also use our framework to find “scrambled” versions of the classical RSK correspondence and to find an RSK correspondence for moon polyominoes. The results extend to limiting models, including the KPZ equation and the Airy sheet.

Funding Statement

D. Dauvergne was supported by an NSERC PDF.


I would like to thank the organizers of the Banff International Research Station workshop on “Dimers, Ising Model and Interactions,” where the striking results of [7] were first brought to my attention. I would like to thank Ivan Corwin, Pavel Galashin, Vadim Gorin, Bálint Virág and Nikolaos Zygouras for helpful comments, discussions and for pointing out connections with other work. I would like to thank Sam Hopkins for suggesting that there might be a connection between this work and [24] and Hugh Thomas for helping me to understand this connection precisely.


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Duncan Dauvergne. "Hidden invariance of last passage percolation and directed polymers." Ann. Probab. 50 (1) 18 - 60, January 2022. https://doi.org/10.1214/21-AOP1527


Received: 1 May 2020; Revised: 1 February 2021; Published: January 2022
First available in Project Euclid: 23 February 2022

MathSciNet: MR4385122
zbMATH: 1499.60328
Digital Object Identifier: 10.1214/21-AOP1527

Primary: 60K35
Secondary: 05A15 , 05A19 , 05E10

Keywords: Airy sheet , Directed polymers , geometric RSK correspondence , KPZ , Last passage percolation , moon polyominoes , Robinson–Schensted correspondence , RSK correspondence

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 1 • January 2022
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