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 \(2+1\) discrete Solid-On-Solid random interfaces above a hard wall.
We dedicate this paper to Anton Bovier on the occasion of his 60th birthday.
DI was supported by the Israeli Science Foundation grants 1723/14 and 765/18.
VW was supported by the Humboldt Foundation.
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Caputo, P., Ioffe, D., Wachtel, V. (2019). Tightness and Line Ensembles for Brownian Polymers Under Geometric Area Tilts. In: Gayrard, V., Arguin, LP., Kistler, N., Kourkova, I. (eds) Statistical Mechanics of Classical and Disordered Systems . StaMeClaDys 2018. Springer Proceedings in Mathematics & Statistics, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-030-29077-1_10
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