Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean

Jingjia Liu () and Quirin Vogel ()
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Jingjia Liu: Universität Münster
Quirin Vogel: University of Warwick

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2315-2345

Abstract: Abstract We prove an upper large deviation bound on the scale of the mean for a symmetric random walk in the plane satisfying certain moment conditions. This result complements the study by Phetpradap for the random walk range, which is restricted to dimension three and higher, and of van den Berg, Bolthausen and den Hollander, for the volume of the Wiener sausage.

Keywords: Large deviations; Random walk range; Planar random walk; Primary 60G50; Secondary 60F10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01039-4

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