Harmonic Analysis Seminar: Matthew Bond
Date
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Topic
Buffon's needle probability for rational product Cantor sets
Speakers
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Abstract:
We investigate the probability that "Buffon's Needle" lands near a one-dimensional self-similar product set in the complex plane, where the similarity maps have rational centers and identical scalings. If the factors A and B are defined by at most 6 similarities, then the likelihood that the needle intersects an e^{-n}-neighborhood of such a set is at most Cn^{-p/\log\log n} for some p>0.