The Annals of Probability

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

Richard F. Bass and Xia Chen

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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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Ann. Probab., Volume 32, Number 4 (2004), 3221-3247.

First available in Project Euclid: 8 February 2005

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Zentralblatt MATH identifier

Primary: 60J55: Local time and additive functionals
Secondary: 60J55: Local time and additive functionals 60F10: Large deviations

Intersection local time Gagliardo–Nirenberg inequality law of the iterated logarithm critical exponent self-intersection local time large deviations


Bass, Richard F.; Chen, Xia. Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm. Ann. Probab. 32 (2004), no. 4, 3221--3247. doi:10.1214/009117904000000504.

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