Year: 2026
Type: preprint
Abstract: Motivated by the study of the level lines of the $(2+1)$D Solid-On-Solid (SOS) model above a floor, near the corners of the box, we derive the limit law of an ensemble of $K$ curves from a $(1+1)$D SOS model, with an area tilt, and above a wedge-shaped floor in $\{-N,\ldots,N\}$. We show that there exist explicit critical points $α_0=1>α_1>\ldots>α_K>0$ such that, for each $r \geq 1$, along the intervals $\pm(α_{r} N,α_{r-1} N)$, the bottom $K+1-r$ curves, rescaled by $(N^{2/3},N^{1/3})$, tend to the law of a Geometrically-Area-Tilted Ensemble of non-crossing Brownian paths (Brownian GATE), independently across those $2K$ intervals. All other curves, centered and rescaled by $(N,\sqrt{N})$, tend to a product of $K$ suitable Brownian bridges.
Source: arXiv (Cornell University)
Authors: Dembo, Amir, Lubetzky, Eyal, Zeitouni, Ofer
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201869437