Given a symmetric random walk in Z2 with finite second moments, let Rn be
the range of the random walk up to time n. We study moderate deviations for
Rn − ERn and ERn − Rn. We also derive the corresponding laws of the iterated
AMS 2000 subject classifications. 60F10, 60G50, 60J55.
Key words and phrases: Range, random walks, intersection local time, moder-
ate deviations, Gagliardo-Nirenberg inequality, law of the iterated logarithm
Richard F. Bass was partially by NSF grant DMS0244737.
Xia Chen was partially supported by NSF grant DMS0704024.
Jay Rosen was partially supported by grants from the NSF and from PSC-
Received by the editor January 28, 2006, and in revised form on September 6,