Abstract
A standard random walk on a one-dimensional integer lattice is considered where the probability ofk self-intersections of a path ω=(0, ω(1),..., ω(n) is proportional toe −λk. It is proven that for λ<0,n −1/3ω(n) converges to a certain continuous random variable. For λ>0 the formulas are given for the asymptotic Westerwater velocity of a generic path and for the variance of the fluctuations about the asymptotic motion.
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Zolądek, H. One-dimensional random walk with self-interaction. J Stat Phys 47, 543–550 (1987). https://doi.org/10.1007/BF01007525
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DOI: https://doi.org/10.1007/BF01007525