The multifractal nature of heterogeneous sums of Dirac masses

• Autores: Julien Barral, Stéphane Seuret
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 144, Nº 3, 2008, págs. 707-727
• Idioma: inglés
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• Resumen

  • This paper investigates the natural problem of performing the multifractal analysis of heterogeneous sums of Dirac masses where (xn)n=0 is a sequence of points in [0, 1]d and (wn)n=0 is a positive sequence of weights such that Sn=0 wn < 8. We consider the case where the points xn are roughly uniformly distributed in [0, 1]d, and the weights wn depend on a random self-similar measure µ, a parameter ? (0, 1], and a sequence of positive radii (?n)n=1 converging to 0 in the following way The measure ? has a rich multiscale structure. The computation of its multifractal spectrum is related to heterogeneous ubiquity properties of the system {(xn,?n)n with respect to µ.