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

Richard F. Bass, Xia Chen

Published 2005-03-25Version 1

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.

Comments: Published at http://dx.doi.org/10.1214/009117904000000504 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2004, Vol. 32, No. 4, 3221-3247
Categories: math.PR
Subjects: 60J55, 60J55, 60F10
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