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Local asymptotic laws for the Brownian convex hull
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  • Published: September 1992

Local asymptotic laws for the Brownian convex hull

  • Davar Khoshnevisan1 

Probability Theory and Related Fields volume 93, pages 377–392 (1992)Cite this article

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Summary

We prove a general theorem for the precise rate at which the convex hull of Brownian motion gets created. The latter result relates large deviation theory to P. Lévy's geometric proof of Strassen's law of the iterated logarithm. This also answers a question of S. Evans. Moreover, we give a partial solution to a question of J. Hammersley and P. Lévy regarding the slowness of the growth of the hull process. Several examples, some classical and some new, are given to illustrate the theorems. Finally, we present applications to the convex hull of random walks ind dimensions.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA, USA

    Davar Khoshnevisan

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  1. Davar Khoshnevisan
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Khoshnevisan, D. Local asymptotic laws for the Brownian convex hull. Probab. Th. Rel. Fields 93, 377–392 (1992). https://doi.org/10.1007/BF01193057

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  • Received: 15 March 1991

  • Revised: 20 December 1991

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01193057

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Mathematics Subject Classification (1985)

  • 60J30
  • 52A30
  • 52A45
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