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Moderate Deviations for the Range of Planar Random Walks
Richard F. Bass, University of Connecticut, Storrs, CT, Xia Chen, University of Tennessee, Knoxville, TN, and Jay Rosen, CUNY, College of Staten Island, NY
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Memoirs of the American Mathematical Society
2009; 82 pp; softcover
Volume: 198
ISBN-10: 0-8218-4287-0
ISBN-13: 978-0-8218-4287-4
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.

• 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