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Mathematics  2005 

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

DOI: 10.1214/009117904000000504

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Abstract:

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.

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