Abstract
In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritzen [J. Chem. Phys. 48 (1968) 3351]. As the system size
Obtaining the shape theorem requires to derive a functional central limit theorem for the excursion of a random walk with Laplace symmetric increments conditioned on sweeping a prescribed geometric area. This result is proven in a companion paper Carmona and Pétrélis (2017).
Citation
Philippe Carmona. Nicolas Pétrélis. "A shape theorem for the scaling limit of the IPDSAW at criticality." Ann. Appl. Probab. 29 (2) 875 - 930, April 2019. https://doi.org/10.1214/18-AAP1396
Information