Abstract

Invariance principle for a Potts interface along a wall D. Ioffe, S. Ott, Y. Velenik, V. Wachtel J. Stat. Phys. 180, 832-861 (2020) (special issue celebrating Joel Lebowitz' 90th birthday). We consider nearest-neighbor two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive scaling, the interface weakly converges to the standard Brownian excursion. Key words: Potts model, random cluster model, interface, Ornstein-Zernike asymptotics, invariance principle, Brownian excursion Files: PDF file, bibtex