HIDDEN INVARIANCE OF LAST PASSAGE PERCOLATION AND DIRECTED POLYMERS

• 成果类型: Article
• 署名作者: Dauvergne, Duncan
• 署名单位: Princeton University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1527
• 发表日期: 2022
• 页码: 18-60
• 关键词: extension; fillings; GROWTH; paths; shape

摘要

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 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.