Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
Richard F. Bass, Xia Chen
Abstract
If βt is renormalized self-intersection local time for planar Brownian motion, we characterize when Eeγβ1 is finite or infinite in terms of the best constant of a Gagliardo-Nirenberg inequality. We prove large deviation estimates for β1 and -β1. We establish lim sup and lim inf laws of the iterated logarithm for βt as t∞.
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