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Dyson Ferrari-Spohn diffusions and ordered walks under area tilts

Ioffe, Dmitry
Wachtel, Vitali
Published in Probability Theory and Related Fields. 2018, vol. 170, no. 1-2, p. 11-47
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 principleCritical prewettingEntropic repulsionOrdered random walksNon-crossing random walksNon-intersecting random walksFerrari-Spohn diffusions
arXiv: 1601.04444
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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 https://archive-ouverte.unige.ch/unige:81093

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Deposited on : 2016-02-29

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