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The law of (1+1)D SOS with an area tilt in a wedge
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,…,N}. We show that there exist explicit critical points α0=1>α1>…>αK>0 such that, for each r ≥ 1, along the intervals ±(αr N,αr−1 N), the bottom K+1−r curves, rescaled by (N2/3,N1/3), 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,√N), tend to a product of K suitable Brownian bridges.
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BibTeX
@misc{dembo2026with,
title = {{The law of (1+1)D SOS with an area tilt in a wedge}},
author = {Amir Dembo and Eyal Lubetzky and Ofer Zeitouni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.05262},
eprint = {2608.05262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.05262},
}
RIS
TY - UNPB
TI - The law of (1+1)D SOS with an area tilt in a wedge
AU - Amir Dembo
AU - Eyal Lubetzky
AU - Ofer Zeitouni
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.05262
UR - https://arxiv.org/abs/2608.05262
AB - 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,…,N}. We show that there exist explicit critical points α_0=1>α_1>…>α_K>0 such that, for each r ≥ 1, along the intervals ±(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,√N), tend to a product of K suitable Brownian bridges.
ER -