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.
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Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.
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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.
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Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.