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

Richard F. Bass, Xia Chen

Type: Article

Publication Date: 2004-10-01

Citations: 40

DOI: https://doi.org/10.1214/009117904000000504

Abstract

If βt is renormalized self-intersection local time for planar Brownian motion, we characterize when $\mathbb{E}e^{\gamma\beta_{1}}$ 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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