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|a UAMI
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|a Shmerkin, Pablo,
|e author.
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|a Spatially independent Martingales, intersections, and applications /
|c Pablo Shmerkin, Ville Suomala.
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| 264 |
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1 |
|a Providence, RI :
|b American Mathematical Society,
|c [2018]
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|c ©2017
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| 300 |
|
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|a 1 online resource (v, 102 pages) :
|b illustrations
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|a Memoirs of the American Mathematical Society,
|x 0065-9266 ;
|v volume 251, number 1195
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| 588 |
0 |
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|a Print version record.
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|a Includes bibliographical references (pages 99-102).
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|a "January 2018, volume 251, number 1195 (second of 6 numbers)."
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0 |
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|a Introduction -- Notation -- The setting -- Holder continuity of intersections -- Classes of spatially independent martingales -- A geometric criterion for Holder continuity -- Affine intersections and projections -- Fractal boundaries and intersections with algebraic curves -- Intersections with self-similar sets and measures -- Dimension of projectiojns: applications of theorem 4.4. -- Upper bounds on dimensions of intersections -- Lower bounds for the dimension of intersections, and dimension conservation -- Products and convolutions of spatially independent martingales -- Applications to Fourier decay and restriction.
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| 590 |
|
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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| 650 |
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0 |
|a Random measures.
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| 650 |
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0 |
|a Martingales (Mathematics)
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| 650 |
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0 |
|a Stochastic processes.
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| 650 |
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0 |
|a Intersection theory (Mathematics)
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| 650 |
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6 |
|a Mesures aléatoires.
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| 650 |
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6 |
|a Martingales (Mathématiques)
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| 650 |
|
6 |
|a Processus stochastiques.
|
| 650 |
|
6 |
|a Théorie des intersections.
|
| 650 |
|
7 |
|a Procesos estocásticos
|2 embne
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| 650 |
0 |
7 |
|a Intersección, Teoría de la
|2 embucm
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| 650 |
|
7 |
|a Intersection theory (Mathematics)
|2 fast
|
| 650 |
|
7 |
|a Martingales (Mathematics)
|2 fast
|
| 650 |
|
7 |
|a Random measures
|2 fast
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| 650 |
|
7 |
|a Stochastic processes
|2 fast
|
| 700 |
1 |
|
|a Suomala, Ville,
|d 1980-
|e author.
|
| 710 |
2 |
|
|a American Mathematical Society,
|e publisher.
|
| 776 |
0 |
8 |
|i Print version record:
|a Shmerkin, Pablo.
|t Spatially independent Martingales, intersections, and applications.
|d Providence, RI : AMS, American Mathematical Society, [2018]
|z 9781470426880
|w (DLC) 2017054242
|w (OCoLC)1019843927
|
| 830 |
|
0 |
|a Memoirs of the American Mathematical Society ;
|v no. 1195.
|
| 856 |
4 |
0 |
|u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5346254
|z Texto completo
|
| 880 |
3 |
|
|6 520-00/(S
|a "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 {ηt}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. Łaba in connection to the restriction problem for fractal measures."--Page v
|
| 880 |
3 |
|
|6 520-00/(S
|a "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 {ηt}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 v
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