The power law for the Buffon needle probability of the four-corner Cantor set
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Publication:3082446
DOI10.1090/S1061-0022-2010-01133-6zbMath1213.28006arXiv0801.2942MaRDI QIDQ3082446
F. L. Nazarov, Yuval Peres, Alexander Volberg
Publication date: 10 March 2011
Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0801.2942
Geometric probability and stochastic geometry (60D05) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Hausdorff and packing measures (28A78)
Related Items (11)
The exact power law for Buffon's needle landing near some random Cantor sets ⋮ Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set ⋮ Transversal families of nonlinear projections and generalizations of Favard length ⋮ The Buffon's needle problem for random planar disk-like Cantor sets ⋮ Circular Favard length of the four-corner Cantor set ⋮ Book review of: P. Mattila, Fourier analysis and Hausdorff dimension ⋮ Some toy Furstenberg sets and projections of the four-corner Cantor set ⋮ Quantitative visibility estimates for unrectifiable sets in the plane ⋮ Plenty of big projections imply big pieces of Lipschitz graphs ⋮ The fractional Riesz transform and an exponential potential ⋮ A quantification of a Besicovitch non-linear projection theorem via multiscale analysis
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- Projecting the one-dimensional Sierpiński gasket
- Self-similar sets of zero Hausdorff measure and positive packing measure
- Tiling the line with translates of one tile
- Tangential properties of sets and arcs of infinite linear measure
- A quantitative version of the Besicovitch projection theorem via multiscale analysis
- The planar Cantor sets of zero analytic capacity and the local 𝑇(𝑏)-Theorem
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