2019/12/31 by Alexei Borodin, Vadim Gorin, Michael Wheeler · 22 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Brownian motion #Combinatorics #Gaussian #Geometry #Graph #Integrable system #Mathematical physics #Mathematical proof #Mathematics #Observable #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Vertex (graph theory) #Vertex model #math-ph #math.CO #math.MP #math.PR
paper · pdf · doi:10.1112/plms.12427
published in Proceedings of the London Mathematical Society 124(2), 182-299 (Wiley) · 102 pages. v2: misprints corrected
arxiv created 2020/01/10 · openalex publication_date 2022/01/20 · arxiv updated 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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–Baxter integrability of the inhomogeneous colored stochastic six-vertex model and Lagrange interpolation. We also show that a simplified (Gaussian) version of our theorems is related to the invariance in law of the local time of the Brownian bridge under the shift of the observation level.