The Arctic Curve for Aztec Rectangles with Defects via the Tangent Method

• Published in: Journal of Statistical Physics
• Main Authors: Di Francesco, Philippe, Guitter, Emmanuel
• Other Authors: Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), NSF grant DMS18-02044, Morris and Gertrude Fine endowment
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2019
• Subjects: [MATH]Mathematics [math]; [PHYS]Physics [physics]; Arctic
• Online Access: https://hal.science/hal-04404664; https://doi.org/10.1007/s10955-019-02315-2

International audience The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated non-intersecting lattice path configurations are made of Schröder paths whose weights involve two parameters and q keeping track respectively of one particular type of step and of the area below the paths. We predict the arctic curve for an arbitrary distribution of defects, and illustrate our result with a number of examples involving different classes of boundary defects.