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

Richard F. Bass; Xia Chen; Jay Rosen

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

Richard F. Bass·Xia Chen·Jay Rosen

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Abstract

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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Richard F. Bass, Xia Chen, Jay Rosen. 2005-06-20. Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks. https://arxiv.org/abs/math/0506414

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