Moderate Deviations for the Range of Planar Random Walks

Given a symmetric random walk in ${\mathbb Z}^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. The authors study moderate deviations for $R_n -{\mathbb E}R_n$ and ${\mathbb E}R_n -R_n$. They also derive the corresponding laws of the iterated logarithm.

• Author: Richard F. Bass, Xia Chen, Jay Rosen
• Publisher: American Mathematical Soc.
• Published: 2009-03-06
• Pages: 98