%0 Journal Article
%T Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
%A Richard F. Bass
%A Xia Chen
%A Jay Rosen
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0506414v1