English

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

Probability 2007-05-23 v1

Abstract

Let B_n be the number of self-intersections of a symmetric random walk with finite second moments in the integer planar lattice. We obtain moderate deviation estimates for B_n - E B_n and E B_n- B_n, which are given in terms of the best constant of a certain Gagliardo-Nirenberg inequality. We also prove the corresponding laws of the iterated logarithm.

Keywords

Cite

@article{arxiv.math/0506414,
  title  = {Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks},
  author = {Richard F. Bass and Xia Chen and Jay Rosen},
  journal= {arXiv preprint arXiv:math/0506414},
  year   = {2007}
}