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arXiv · 2201.01635

On the limiting law of line ensembles of Brownian polymers with geometric area tilts

Amir Dembo·Eyal Lubetzky·Ofer Zeitouni
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Abstract

We study the line ensembles of non-crossing Brownian bridges above a hard wall, each tilted by the area of the region below it with geometrically growing pre-factors. This model, which mimics the level lines of the $(2+1)$D SOS model above a hard wall, was studied in two works from 2019 by Caputo, Ioffe and Wachtel. In those works, the tightness of the law of the top $k$ paths, for any fixed $k$, was established under either zero or free boundary conditions, which in the former setting implied the existence of a limit via a monotonicity argument. Here we address the open problem of a limit under free boundary conditions: we prove that as the interval length, followed by the number of paths, go to $\infty$, the top $k$ paths converge to the same limit as in the free boundary case, as conjectured by Caputo, Ioffe and Wachtel.

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Amir Dembo, Eyal Lubetzky, Ofer Zeitouni. 2022-05-10. On the limiting law of line ensembles of Brownian polymers with geometric area tilts. https://arxiv.org/abs/2201.01635

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