Abstract
We prove that if the origin is translated so that the real axis is tangential to the (random) convex hull of a planar Brownian motion, touching at the origin, then for each positive \(\frac{{(\frac{\pi }{2} + \varepsilon )|x|\log ^3 (1/|x|)}}{{\log (1/|x|)}}\) is an upper function for the hull but \(\frac{{(\frac{\pi }{2} - \varepsilon )|x|\log ^3 (1/|x|)}}{{\log (1/|x|)}}\) is not.
Research partially supported by NSF Grant DMS-86-01800.
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References
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© 1992 Springer-Verlag
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Mountford, T.S. (1992). A critical function for the planar Brownian convex hull. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVI. Lecture Notes in Mathematics, vol 1526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084314
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DOI: https://doi.org/10.1007/BFb0084314
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