Details

Autor(en) / Beteiligte

• Ioffe, Dmitry
• Velenik, Yvan
• Wachtel, Vitali

Titel

Dyson Ferrari–Spohn diffusions and ordered walks under area tilts

Ist Teil von

• Probability theory and related fields, 2018-02, Vol.170 (1-2), p.11-47

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2018

Link zum Volltext

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• 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.