English

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

Probability 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0503592,
  title  = {Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm},
  author = {Richard F. Bass and Xia Chen},
  journal= {arXiv preprint arXiv:math/0503592},
  year   = {2007}
}

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)

R2 v1 2026-07-22T17:17:20.847Z