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Hidden invariance of last passage percolation and directed polymers

Hidden invariance of last passage percolation and directed polymers

Last passage percolation and directed polymer models on ℤ 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 …