HIDDEN INVARIANCE OF LAST PASSAGE PERCOLATION AND DIRECTED POLYMERS

Duncan Dauvergne

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Last passage percolation and directed polymer models on Z2 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 can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance statements for last passage times, geodesic locations, disjointness probabilities, polymer partition functions and quenched polymer measures. We also use our framework to find “scrambled” versions of the classical RSK correspondence and to find an RSK correspondence for moon polyominoes. The results extend to limiting models, including the KPZ equation and the Airy sheet

Original languageEnglish (US)
Pages (from-to)18-60
Number of pages43
JournalAnnals of Probability
Volume50
Issue number1
DOIs
StatePublished - Jan 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Airy sheet
  • Directed polymers
  • Geometric rsk correspondence
  • Kpz
  • Last passage percolation
  • Moon polyominoes
  • Robinson–schensted correspondence
  • Rsk correspondence

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