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LIMSUP RANDOM FRACTALS AND APPLICATIONS
Yimin Xiao
University of Utah
February 26, JWB 208, 305 p.m.
Abstract
Many random sets such as the set of fast points of Brownian motion,
the set of thick points of the sojourn measure of spatial Brownian motion
and the set of exceptional growth of the branching measure on a Galton-Watson
tree can be well approximated by limsup random fractals. In this talk, we will
show that, under some mild conditions, the hitting probabilities of a limsup
random fractal $A$ are determined by the packing dimension of the target set
$E$, rather than its Hausdorff dimension. When $A \cap E \ne \emptyset$, we
give results on the Hausdorff dimension and packing dimension of $A \cap E$.
Some applications of these results to limit laws and functional limit laws
of Brownian motion and other Gaussian processes will also be discussed.
This is recent joint work with D. Khoshnevisan of the University of
Utah and Y. Peres of the University of California at Berkeley and the
Hebrew University.