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Scientific article
English

Dyson Ferrari-Spohn diffusions and ordered walks under area tilts

Published inProbability theory and related fields, vol. 170, no. 1-2, p. 11-47
Publication date2018
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.

Keywords
  • Invariance principle
  • Critical prewetting
  • Entropic repulsion
  • Ordered random walks
  • Non-crossing random walks
  • Non-intersecting random walks
  • Ferrari-Spohn diffusions
Classification
  • arxiv : math.PR
Citation (ISO format)
IOFFE, Dmitry, VELENIK, Yvan, WACHTEL, Vitali. Dyson Ferrari-Spohn diffusions and ordered walks under area tilts. In: Probability theory and related fields, 2018, vol. 170, n° 1-2, p. 11–47. doi: 10.1007/s00440-016-0751-z
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Article (Submitted version)
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Identifiers
ISSN of the journal0178-8051
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