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

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  • Jingjia Liu

    (Universität Münster)

  • Quirin Vogel

    (University of Warwick)

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.

Suggested Citation

  • Jingjia Liu & Quirin Vogel, 2021. "Large Deviations of the Range of the Planar Random Walk on the Scale of the Mean," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2315-2345, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01039-4
    DOI: 10.1007/s10959-020-01039-4
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    References listed on IDEAS

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    1. Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
    2. Bolthausen, Erwin, 1987. "Markov process large deviations in [tau]-topology," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 95-108.
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