Random walk versus random line

Joël De Coninck, François Dunlop and Thierry Huillet

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 19, 4034-4040

Abstract: We consider random walks Xn in Z+, obeying a detailed balance condition, with a weak drift towards the origin when Xn↗∞. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are discussed in terms of recurrence versus wetting. A drift −δXn−1+O(Xn−2) of the random walk yields a Solid-On-Solid potential with an attractive well at the origin and a repulsive tail δ(2+δ)8Xn−2+O(Xn−3) at infinity, showing complete wetting for δ≤1 and critical partial wetting for δ>1.

Keywords: Random walk; Recurrence; SOS model; Pinning; Wetting (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:19:p:4034-4040

DOI: 10.1016/j.physa.2009.06.030

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