Confinement of Brownian Polymers under Geometric Area Tilts

TL;DR

This paper studies the behavior of non-colliding Brownian bridges constrained by geometric area tilts, modeling level lines of 2+1 discrete Solid-On-Solid interfaces near a hard wall.

Contribution

It introduces a new model for non-colliding Brownian bridges with geometric area tilts to analyze their tightness and behavior near a hard wall.

Findings

Established tightness of the family of processes

Connected the model to level lines of discrete interfaces

Provided insights into the effect of geometric area tilts

Abstract

We consider tightness for families of non-colliding Brownian bridges above a hard wall, which are subject to geometrically growing self-potentials of tilted area type. The model is introduced in order to mimic level lines of $2+1$ discrete Solid-On-Solid random interfaces above a hard wall.