Spatially independent Martingales, intersections, and applications / Pablo Shmerkin, Ville Suomala

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Memoirs of the American Mathematical Society ; volume 251, number 1195Publisher: Providence, RI : American Mathematical Society, 2018Description: 1 Online-Ressource (v, 102 pages)Subject(s): Additional physical formats: 1470426889 | 9781470426880 | 1470442647 | 9781470442644 | Erscheint auch als: No title Druck-Ausgabe | Print version record: Spatially independent Martingales, intersections, and applications. Providence, RI : AMS, American Mathematical Society, [2018]DDC classification:
  • 519.2/36
LOC classification:
  • QA274.46
Online resources: Summary: "We 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. We pair the random measures with deterministic families of parametrized measures {{u03B7}t}t, and show that under some natural checkable conditions, a.s. the mass of the intersections is Hölder continuous as a function of t. 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 we 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, (d) rapid Fourier decay. Among other applications, we obtain an answer to a question of I. Laba in connection to the restriction problem for fractal measures."--Page vPPN: PPN: 1026211255Package identifier: Produktsigel: ZDB-4-NLEBK
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