Almost Sure
@Almost_Sure
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George Lowther, Author of Almost Sure blog, on maths, probability and stochastic calculus. Also on YouTube https://t.co/VyOijwbe9l
London, UK
Joined September 2020
New video released on the Gaussian correlation inequality. This unexpected proof shocked mathematicians!. link below
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RT @DeepDishEnjoyer: i tried reading her paper but couldn't lol.some 17 year olds are so cracked.
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Evidence Terrence Howard is now working at my local Tesco. (there’s a whole shelf of these)
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These two lovebirds have been living on my garden fence for at least 3 years, since I bought the house!. They’re like part of the family now, maybe I should name them?
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So before this guy, shelves just kept falling down?.
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Obviously lots of technical details, but it seemed like a very satisfying way to prove it.
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So passing to dual twice gets you back where you started, so an equivalence. The functions on original space are Fourier transform of functions on dual space, so also proves Fourier inversion.
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I’m not sure of other proofs, but I once proved Pontryagin duality myself. Define *-algebra of C-valued functions on the space, under multiplication and complex conjugation. Also a *-algebra under convolution & group inversion. Passing to dual group exchanges these operations.
@TopologyFact more generally, Potryagin duality is an equivalence between locally compact Hausdorff abelian groups and itself (dually). And, this gives the dual equivalence. compact <-> discrete.
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I once asked about this on Physics Forums, many years ago, and Tsirelson himself (RIP) answered!. He didn’t know of any physical reasons for it other than, that’s what quantum theory gives though.
We’ve all heard of Bell’s inequality which is satisfied by local classical theories in physics, but violated by Quantum Theory. But, have you heard of the (mysterious) Tsirelson’s inequality?.This is a weaker bound than Bell’s, but is required for Quantum Theory to be true.
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No violations of Tsirelson’s bound have ever been observed. Obviously…otherwise it would contradict quantum theory. On the other hand, other than the fact that it follows from quantum theory, I know of no physical principal requiring it.
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We’ve all heard of Bell’s inequality which is satisfied by local classical theories in physics, but violated by Quantum Theory. But, have you heard of the (mysterious) Tsirelson’s inequality?.This is a weaker bound than Bell’s, but is required for Quantum Theory to be true.
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he is a bit left wing, so no doubt the right wingers on here will disagree with some stuff he says. But, it’s fun seeing some real grifters taken down a few pegs!.
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this is just annoying. First he introduces various terms in written English, representing them by letters. M,X,G. Then, never actually refers to these letters again. And the very next sentence, suddenly uses a bunch of letters and symbols, without saying what they mean!.
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