17 citations · 22 across the 6 of their papers we have counts for
5 papers · 1 filter
Quantitative visibility estimates for unrectifiable sets in the plane
M. Bond, I. Laba, J. Zahl
The "visibility" of a planar set from a point is defined as the normalized size of the radial projection of from to the unit circle centered at . Simon and Solom…
Buffon's needle estimates for rational product Cantor sets
Matthew Bond, Izabella Laba, Alexander Volberg
Let be a self-similar product Cantor set in the complex plane, defined via , where $T_j:\C\to\C$ have the…
Buffon needle lands in -neighborhood of a 1-Dimensional Sierpinski Gasket with probability at most
Matt Bond, Alexander Volberg
In recent years, relatively sharp quantitative results in the spirit of the Besicovitch projection theorem have been obtained for self-similar sets by studying the norms of t…
The Power Law For Buffon's Needle Landing Near the Sierpinski Gasket
Matthew Bond, Alexander Volberg
In this paper we get a power estimate from above of the probability that Buffon's needle will land within distance 3^{-n} of Sierpinski's gasket of Hausdorff dimension 1. In compar…
Buffon needles landing near Sierpinski gasket
Matthew Bond, Alexander Volberg
In this paper we modify the method of Nazarov, Peres, and Volberg "The power law for the Buffon needle probability of the four-corner Cantor set", arXiv:0801.2942, to get an estima…