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Confinement of Brownian polymers under geometric area tilts. (English) Zbl 1466.60068
Summary: We consider confinement properties of 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.

MSC:
60F17 Functional limit theorems; invariance principles
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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