Integrable last passage percolation and directed polymers on Z^2 gain shift and rearrangement invariances from RSK correspondences plus decoupling, yielding scrambled RSK versions, moon polyomino RSK, and extensions to KPZ and Airy sheet.
The geometric Burge correspondence and the partition funct ion of polymer replicas
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Hidden invariance of last passage percolation and directed polymers
Integrable last passage percolation and directed polymers on Z^2 gain shift and rearrangement invariances from RSK correspondences plus decoupling, yielding scrambled RSK versions, moon polyomino RSK, and extensions to KPZ and Airy sheet.