%0 Journal Article
%T Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
%A Richard F. Bass
%A Xia Chen
%J Mathematics
%D 2005
%I arXiv
%R 10.1214/009117904000000504
%X If \beta_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{\gamma\beta_1} is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for \beta_1 and -\beta_1. We establish lim sup and lim inf laws of the iterated logarithm for \beta_t as t\to\infty.
%U http://arxiv.org/abs/math/0503592v1