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 \(\mathbb {E}X_{n}\sim\mathrm{const.}\,n^{1-{\delta \over2}}\) 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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De Coninck, J., Dunlop, F. & Huillet, T. Random Walk Weakly Attracted to a Wall. J Stat Phys 133, 271–280 (2008). https://doi.org/10.1007/s10955-008-9609-9
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DOI: https://doi.org/10.1007/s10955-008-9609-9