# Tightness and Line Ensembles for Brownian Polymers under Geometric Area Tilts

## TL;DR

This paper establishes tightness and describes the limiting behavior of non-colliding Brownian bridge line ensembles with geometric area tilts, modeling (2+1)-D solid-on-solid interfaces with self-potentials.

## Contribution

It introduces a new model of line ensembles with geometric area tilts and proves their tightness and Brownian-Gibbs properties, extending understanding of interface models.

## Key findings

- Proved tightness of the line ensembles.
- Derived Brownian-Gibbs description of the limit.
- Demonstrated distinct statistical properties from classical non-colliding Brownian bridges.

## Abstract

We prove tightness and limiting Brownian-Gibbs description for line ensembles of non-colliding Brownian bridges above a hard wall, which are subject to geometrically growing self-potentials of tilted area type. Statistical properties of the resulting ensemble are very different from that of non-colliding Brownian bridges without self-potentials. The model itself was introduced in order to mimic level lines of (2+1)-dimensional discrete Solid-On-Solid random interfaces above a hard wall.