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On the Hausdorff dimension of exceptional random sets generated by multivariate spacings

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Abstract

We consider multivariate spacings blocks in the usual sense (refer to Deheuvels (Z Wahrsch Verw Gebiete 64:411–424, 1983)). We consider the sets of exceptional points in the neighborhood of which such spacings are, infinitely often, unusually large. Our main result, in the spirit of Hawkes (Math Proc Camb Phil Soc 293–303, 1981), shows that these sets constitute random fractals, whose Hausdorff dimensions are explicitly evaluated.

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  1. LSTA Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013, Paris, France

    Claire Coiffard

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  1. Claire Coiffard
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Correspondence to Claire Coiffard.

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Coiffard, C. On the Hausdorff dimension of exceptional random sets generated by multivariate spacings. Metrika 73, 359–371 (2011). https://doi.org/10.1007/s00184-009-0282-z

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  • DOI: https://doi.org/10.1007/s00184-009-0282-z

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