Resumen de The multifractal nature of heterogeneous sums of Dirac masses
Julien Barral, Stéphane Seuret
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.
