Memoirs of the American Mathematical Society 2009; 82 pp; softcover Volume: 198 ISBN10: 0821842870 ISBN13: 9780821842874 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/198/929
 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. Table of Contents  Introduction
 History
 Overview
 Preliminaries
 Moments of the range
 Moderate deviations for \(R_n{\mathbb E}R_n\)
 Moderate deviations for \({\mathbb E}R_n R_n\)
 Exponential asymptotics for the smoothed range
 Exponential approximation
 Laws of the iterated logarithm
 Bibliography
