Self-intersection local time: Critical exponent, large deviations and laws of the iterated logarithm

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 → ∞. 1. Introduction. Le