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Hamiltonians on random walk trajectories

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  • Ferrari, Pablo A.
  • Martínez, Servet

Abstract

We consider Gibbs measures on the set of paths of nearest-neighbors random walks on . The basic measure is the uniform measure on the set of paths of the simple random walk on and the Hamiltonian awards each visit to site by an amount , . We give conditions on ([alpha]x) that guarantee the existence of the (infinite volume) Gibbs measure. When comparing the measures in with the corresponding measures in , the so-called entropic repulsion appears as a counting effect.

Suggested Citation

  • Ferrari, Pablo A. & Martínez, Servet, 1998. "Hamiltonians on random walk trajectories," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 47-68, October.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:1:p:47-68
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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.
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    Cited by:

    1. Ferrari, Pablo A. & Fontes, Luiz R. G. & Niederhauser, Beat M. & Vachkovskaia, Marina, 2004. "The serial harness interacting with a wall," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 175-190, November.
    2. 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.
    3. Littin, Jorge & Martínez, Servet, 2010. "R-positivity of nearest neighbor matrices and applications to Gibbs states," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2432-2446, December.

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