Dyson Ferrari--Spohn diffusions and ordered walks under area tilts

Abstract

We consider families of non-colliding random walks above a hard wall, which are subject to a self-potential of tilted area type. We view such ensembles as effective models for the level lines of a class of $2+1$-dimensional discrete-height random surfaces in statistical mechanics. We prove that, under rather general assumptions on the step distribution and on the self-potential, such walks converge, under appropriate rescaling, to non-intersecting Ferrari--Spohn diffusions associated with limiting Sturm--Liouville operators. In particular, the limiting invariant measures are given by the squares of the corresponding Slater determinants.

33 pages

References in corpus (4)

• Constrained Brownian motion: Fluctuations away from circular and parabolic barriers
• An invariance principle to Ferrari-Spohn diffusions
• Interaction versus entropic repulsion for low temperature Ising polymers
• On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature

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• Scaling limit for line ensembles of random walks with geometric area tilts
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