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A Quantized Johnson Lindenstrauss Lemma: The Finding of Buffon's Needle
[article]

Laurent Jacques

2015
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arXiv
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pre-print

In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening *problem*: What is the probability that a *needle* thrown randomly on a ...
In this work, we show that the solution to this *problem*, and its generalization to $N$ dimensions, allows us to discover a quantized form of the Johnson-Lindenstrauss (JL) Lemma, i.e., one that combines ...
reduce that distortion by a factor √ M . 3 *Buffon's* *needle* *problem*
Initial formulation and solution Let us rephrase *Buffon's* *needle* *problem* stated in the Introduction in a more formal way. ...

arXiv:1309.1507v6
fatcat:p7slt7fcqbhkzfir6yjbwzlty4