Monday, August 8, 2016

A Unified Theory of Randomness

Sheffield and Miller have already posted the first two papers in their proof of the equivalence between LQG and the Brownian map on the scientific preprint site; they intend to post the third and final paper later this summer. The work turned on the ability to reason across different random shapes and processes — to see how random noncrossing curves, random growth, and random two-dimensional surfaces relate to one another. It’s an example of the increasingly sophisticated results that are possible in the study of random geometry.

“It’s like you’re in a mountain with three different caves. One has iron, one has gold, one has copper — suddenly you find a way to link all three of these caves together,” said Sheffield. “Now you have all these different elements you can build things with and can combine them to produce all sorts of things you couldn’t build before.”

- More Here

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