Shift‐invariance for vertex models and polymers

  title={Shift‐invariance for vertex models and polymers},
  author={Alexei Borodin and Vadim Gorin and Michael Wheeler},
  journal={Proceedings of the London Mathematical Society},
We establish a symmetry in a variety of integrable stochastic systems: certain multi‐point distributions of natural observables are unchanged under a shift of a subset of observation points. The property holds for stochastic vertex models, (1+1)d directed polymers in random media, last passage percolation, the Kardar–Parisi–Zhang equation, and the Airy sheet. In each instance it leads to computations of previously inaccessible joint distributions. The proofs rely on a combination of the Yang… 
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  • S. Korotkikh
  • Mathematics
    Probability Theory and Related Fields
  • 2022
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