Random walk versus random line
نویسندگان
چکیده
Joël De Coninck, François Dunlop, Thierry Huillet Abstract: We consider random walks Xn in Z+, obeying a detailed balance condition, with a weak drift towards the origin when Xn ր ∞. 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 −δX n +O(X −2 n ) of the random walk yields a Solid-On-Solid potential with an attractive well at the origin and a repulsive tail δ(2+δ) 8 X −2 n +O(X −3 n ) at infinity, showing complete wetting for δ ≤ 1 and critical partial wetting for δ > 1.
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