Random walk versus random line

Joel De Coninck; Francois Dunlop; Thierry Huillet

doi:10.1016/j.physa.2009.06.030

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arXiv · 0904.2440

Random walk versus random line

Joel De Coninck·Francois Dunlop·Thierry Huillet

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Abstract

We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. 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 -delta/X_n of the random walk yields a Solid-On-Solid potential with an attractive well at the origin and a repulsive tail delta(delta+2)/(8X_n^2) at infinity, showing complete wetting for delta<=1 and critical partial wetting for delta>1.

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Joel De Coninck, Francois Dunlop, Thierry Huillet. 2009-04-16. Random walk versus random line. https://doi.org/10.1016/j.physa.2009.06.030

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