arXiv 1306.38472013-06-17math.DSmath.PR

The geometry of fractal percolation

Michal Rams, Károly Simon

备注：: Survey submitted for AFRT2012 conference

英文摘要：

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions: {itemize} the statements work for all directions, not almost all, the statements are true for more general projections, for example radial projections onto a circle, in the case $\dim_H >1$, each projection has not only positive Lebesgue measure but also has nonempty interior. {itemize}

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