Weakly pinned random walk on the wall: Pathwise descriptions of the phase transition

Stochastic Processes and their Applications

Volumn 96, Issue 2, 2001, Pages 261-284

  Isozaki, Yasuki ^a   Yoshida, Nobuo ^b  

^a OSAKA UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Entropic repulsion; Limit theorems; Random walk; Wall condition; Weak pinning; Wetting transition

Indexed keywords

EID: 0038772546     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(01)00118-1     Document Type: Article

References (17)

1. Belkin B. An invariance principle for conditioned recurrent random walk attracted to a stable law. Z. Wahrsch. verw. Gebiete. 21:1972;45-64.
2. Billingsley P., Tops ø e F. Uniformity in weak convergence. Z. Wahrsch. verw. Gebiete. 7:1967;1-16.
3. Bolthausen, E., 1999. A lecture delivered at the Third Brazilian School of Probability.
4. Bolthausen E., Deuschel J.D., Zeitouni O. Absence of wetting transition for a pinned harmonic crystals in dimension three of larger. J. Math. Phys. 41:2000;1211-1223.
5. Burkhardt T.W. Localization-delocalization transition in a solid-on-solid model with a pinning potential. J. Phys. A: Math. Gen. 14:1981;L63-L68.
6. Caputo P., Velenik Y. A note on wetting transition for gradient fields. Stoch. Proc. Appl. 87(1):2000;107-113.
7. Chalker J.T. The pinning of an interface by a planar defect. J. Phys. A: Math. Gen. 15:1982;L481-L485.
8. Deuschel J.D., Velenik Y. Non-Gaussian interface pinned by a weak potential. Probab. Theory Related Fields. 116:2000;359-377.
9. Dunlop F., Magnen J., Rivasseau V., Roche P. Pinning of an interface by a weak potential. J. Stat. Phys. 66(1/2):1992;71-98.
10. Feller W. An Introduction to Probability Theory and Its Applications II. 2nd Edition. 1970;Wiley, New York.
11. Fisher M.E. Walks, walls, wetting, and melting. J. Stat. Phys. 34(5/6):1984;667-729.
12. Iglehart D.L. Functional central limit theorem for random walks conditioned to stay positive. Ann. Probab. 2(4):1974;608-619.
13. Ioffe D., Velenik Y. A note on the decay of correlations under. δ -pinning Probab. Theory Related Fields. 116:2000;379-389.
14. Karatzas I., Shreve S.E. Brownian Motion and Stochastic Calculus. 2nd Edition:1991;Springer, Berlin.
15. Reed M., Simon B. Method of Modern Mathematical Physics IV. 1978;Academic Press, New York.
16. Upton, P.J., 1999. Exact interface model for wetting in the planar Ising model, Phys. Rev. E 60 (4), R3475-R3478.
17. van Leeuwen J.M.J., Hilhorst H.J. Pinning of rough interface by an external potential. Phys. A. 107(2):1981;319-329.