Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

Details Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

2005-06-20

arxiv.org/abs/math/0506414v1

Mathematics

Probability

Scientific paper

Let B_n be the number of self-intersections of a symmetric random walk with
finite second moments in the integer planar lattice. We obtain moderate
deviation estimates for B_n - E B_n and E B_n- B_n, which are given in terms of
the best constant of a certain Gagliardo-Nirenberg inequality. We also prove
the corresponding laws of the iterated logarithm.

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