Matthew Bond

activity

20082013

most citedQuantitative visibility estimates for unrectifiable sets in the plane

17 citations · 22 across the 6 of their papers we have counts for

collaborators

7 papers

math.CA2013★ 17 cited

Quantitative visibility estimates for unrectifiable sets in the plane

M. Bond, I. Laba, J. Zahl

The "visibility" of a planar set $S$ from a point $a$ is defined as the normalized size of the radial projection of $S$ from $a$ to the unit circle centered at $a$ . Simon and Solom…

math.CA2011★ 3 cited

Buffon's needle estimates for rational product Cantor sets

Matthew Bond, Izabella Laba, Alexander Volberg

Let $S_{\infty} = A_{\infty} \times B_{\infty}$ be a self-similar product Cantor set in the complex plane, defined via $S_{\infty} = ⋃_{j = 1}^{L} T_{j} (S_{\infty})$ , where $T_j:\C\to\C$ have the…

math.CA2009

Buffon needle lands in $ε$ -neighborhood of a 1-Dimensional Sierpinski Gasket with probability at most $∣ lo g ε ∣^{- c}$

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 $L^{p}$ norms of t…

math.CA2009★ 1 cited

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…

math.AP2009

Buffon's needle landing near Besicovitch irregular self-similar sets