Abstract

Dyson Ferrari-Spohn diffusions and ordered walks under area tilts D. Ioffe, Y. Velenik, V. Wachtel Probability Theory and Related Fields 170, 11-47 (2018). 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. Key words: Invariance principle, critical prewetting, entropic repulsion, oredered random walks, non-crossing random walks, non-intersecting random walks, Ferrari-Spohn diffusions Files: PDF file, Published version, bibtex