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Let (Xt, t ≥ 0) be an α-stable random walk with values in Z d. Let lt(x) = t 0 δx(Xs)ds be its local time. For p > 1, not necessarily integer, It = x l p t (x) is the so-called p-fold self-intersection local time of the random walk. When p(d − α) < d, we derive precise logarithmic asymptotics of the probability P [It ≥ rt] for all scales rt E [It]. Our(More)
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