Abstract
We consider the model of a directed polymer pinned to a line of i.i.d. random charges, and focus on the interior of the delocalized phase. We first show that in this region, the partition function remains bounded. We then prove that for almost every environment of charges, the probability that the number of contact points in [0, n] exceeds clogn tends to 0 as n tends to infinity. The proofs rely on recent results of Birkner, Greven, den Hollander (2010) and Cheliotis, den Hollander (2010).
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References
Q. Berger, H. Lacoin, Sharp critical behavior for pinning model in random correlated environment. Preprint, To appear in Stochastic Processes and their Applications http://dx.doi.org/10.1016/j.spa.2011.12.007, arXiv:1104.4969v1 (2011)
M. Birkner, R. Sun, Annealed vs quenched critical points for a random walk pinning model. Ann. Inst. Henri Poincaré Probab. Stat. 46(2), 414–441 (2010)
M. Birkner, A. Greven, F. den Hollander, Quenched large deviation principle for words in a letter sequence. Probab. Theory Related Fields 148 (3–4), 403–456 (2010)
D. Cheliotis, F. den Hollander, Variational characterization of the critical curve for pinning of random polymers. Preprint, To appear at Annals of Probability, arXiv:1005.3661v1 (2010)
G. Giacomin, Random Polymer Models (Imperial College Press, London, 2007)
G. Giacomin, F.L. Toninelli, Estimates on path delocalization for copolymers at selective interfaces. Probab. Theory Related Fields 133(4), 464–482 (2005)
F. den Hollander, in Random Polymers. Ecole d’été de probabilités de Saint Flour XXXVII. Lecture Notes in Mathematics, vol. 1974 (Springer, Berlin, 2009)
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Mourrat, JC. (2012). On the Delocalized Phase of the Random Pinning Model. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_18
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DOI: https://doi.org/10.1007/978-3-642-27461-9_18
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