Large deviations for intersection local times in critical dimension
نویسندگان
چکیده
منابع مشابه
Large deviations for intersection local times in critical dimension
Let (X t , t ≥ 0) be a continuous time simple random walk on Z d , and let l T (x) be the time spent by (X t , t ≥ 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I T = x∈Z d l T (x) q in the critical dimension d = 2q q−1. When q is integer, we obtain similar results for the intersection local times of q independent simple random ...
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Let (Xt, t ≥ 0) be a simple symmetric random walk on Z and for any x ∈ Z, let lt(x) be its local time at site x. For any p > 1, we denote by It = ∑ x∈Zd lt(x) p the p-fold self-intersection local times (SILT). Becker and König [6] recently proved a large deviations principle for It for all p > 1 such that p(d − 2/p) < 2. We extend these results to a broader scale of deviations and to the whole ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2010
ISSN: 0091-1798
DOI: 10.1214/09-aop499