Random Walk Weakly Attracted to a Wall |
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| Authors: | Joël De Coninck François Dunlop Thierry Huillet |
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| Institution: | (1) Centre de Recherche en Modélisation Moléculaire, Université de Mons-Hainaut, 20 Place du Parc, 7000 Mons, Belgium;(2) Laboratoire de Physique Théorique et Modélisation (CNRS–UMR 8089), Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France |
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| Abstract: | We consider a random walk X
n
in ℤ+, starting at X
0=x≥0, with transition probabilities and X
n+1=1 whenever X
n
=0. We prove
as n
↗∞ when δ∈(1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk. |
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| Keywords: | Random walk Orthogonal polynomials Pinning Wetting |
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