Spatially Independent Martingales Intersections and Applications is popular PDF and ePub book, written by Pablo Shmerkin in 2018-02-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Spatially Independent Martingales Intersections and Applications can be Read Online from any device for your convenience.
Spatially Independent Martingales Intersections and Applications Book PDF Summary
The authors define a class of random measures, spatially independent martingales, which we view as a natural generalization of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian cut-outs. The authors pair the random measures with deterministic families of parametrized measures , and show that under some natural checkable conditions, a.s. the mass of the intersections is Hölder continuous as a function of . This continuity phenomenon turns out to underpin a large amount of geometric information about these measures, allowing us to unify and substantially generalize a large number of existing results on the geometry of random Cantor sets and measures, as well as obtaining many new ones. Among other things, for large classes of random fractals they establish (a) very strong versions of the Marstrand-Mattila projection and slicing results, as well as dimension conservation, (b) slicing results with respect to algebraic curves and self-similar sets, (c) smoothness of convolutions of measures, including self-convolutions, and nonempty interior for sumsets, and (d) rapid Fourier decay. Among other applications, the authors obtain an answer to a question of I. Łaba in connection to the restriction problem for fractal measures.
Detail Book of Spatially Independent Martingales Intersections and Applications PDF
- Author : Pablo Shmerkin
- Release : 22 February 2018
- Publisher : American Mathematical Soc.
- ISBN : 9781470426880
- Genre : Mathematics
- Total Page : 114 pages
- Language : English
- PDF File Size : 21,5 Mb
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