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.
Color-position symmetry in interacting particle systems
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abstract
We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to apply the result to colored (or multi-species) ASEP and stochastic vertex models for a certain class of initial/boundary conditions, generalizing previous results of Amir-Angel-Valko and Borodin-Wheeler. We are also able to use the symmetry, together with previously known results for uncolored models, to find novel asymptotic behavior of the second class particles in several situations.
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math.PR 1years
2020 1verdicts
UNVERDICTED 1representative citing papers
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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.