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

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

2005-03-25

arxiv.org/abs/math/0503592v1

Annals of Probability 2004, Vol. 32, No. 4, 3221-3247

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000504 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000504

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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