Moderate deviations for the range of planar random walks

Abstract

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

References in corpus (2)

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
• Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks