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math.AP2022★ 2 cited
The Buffon's needle problem for random planar disk-like Cantor sets
Dimitris Vardakis, Alexander Volberg
We consider a model of randomness for self-similar Cantor sets of finite and positive -Hausdorff measure. We find the sharp rate of decay of the probability that a Buffon needle…
math.AP2019
Geometry of planar curves intersecting many lines in a few points
Dimitris Vardakis, Alexander Volberg
The local Lipschitz property is shown for the graph avoiding multiple point intersection with lines directed in a given cone. The assumption is much stronger than those of Marstran…