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Random Matrix Theory in New Scientist April 14, 2010

Posted by Sarah in Uncategorized.
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Andrew Gelman adds his insights to this New Scientist cover article by Mark Buchanan on random matrix theory.

Currently I’ve been interested in precisely the kinds of results mentioned in the article — I’m using them for my cryo-EM project. I don’t have much to add, since Gelman and Buchanan both do a beautiful job of exposition, except to say that this is the kind of writing about mathematics that I want to see more of. It’s written for a popular audience but doesn’t misrepresent the theory — moreover, it conveys the point that the math has implications for how we come to believe things. It’s not merely a toolbox, it’s a way of revising how we draw conclusions from data, which affects how we predict things like economic trends. And math also informs the other sciences about the limits of what they can infer.

Related is this recent paper, which deals with perturbations of random matrices — we can think of this as a signal matrix plus a noisy random matrix — and shows that if the signal is low rank and sufficiently strong compared to the noise, then the top eigenvalues do correspond to signal rather than noise. It’s a sort of optimistic counterpoint to the pessimistic results of Bouchaud and others mentioned in the article.

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