2016/01/18 by Dmitry Ioffe, Yvan Velenik, Vitali Wachtel · 1 citation
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:60G50 #msc:60F17
paper · pdf · doi:10.1007/s00440-016-0751-z
published as Probab. Theory Relat. Fields (2018) 170: 11 · 33 pages
arxiv created 2016/01/18 · arxiv updated 2018/04/26
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.