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Random walk versus random line

Author

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  • De Coninck, Joël
  • Dunlop, François
  • Huillet, Thierry

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.

Suggested Citation

  • De Coninck, Joël & Dunlop, François & Huillet, Thierry, 2009. "Random walk versus random line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4034-4040.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:19:p:4034-4040
    DOI: 10.1016/j.physa.2009.06.030
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    References listed on IDEAS

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    1. van Leeuwen, J.M.J. & Hilhorst, H.J., 1981. "Pinning of a rough interface by an external potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(2), pages 319-329.
    2. Isozaki, Yasuki & Yoshida, Nobuo, 2001. "Weakly pinned random walk on the wall: pathwise descriptions of the phase transition," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 261-284, December.
    3. Ferrari, Pablo A. & Martínez, Servet, 1998. "Hamiltonians on random walk trajectories," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 47-68, October.
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