Abstract 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 logarithm. 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- CUNY. Received by the editor January 28, 2006, and in revised form on September 6, 2006. vii
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