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anyone wanna talk about how applying the central limit theorem to a random walk in 2D reproduces the euclidean metric starting from a *grid* it’s fucked up and wrong and i’m still trying to figure out what it means

irα!!

@solarsystern

can u send me a link that explains this a lil past 280 characters i feel like i'm 80% towards understanding why this sucks

idk a place where this is spelled out but like okay take a random walk on a 2D square grid where you go up, down, left or right with probability 1/4 each. sample the walk a bunch of times and make a plot of where you end up after like a million steps. you’ll get a 2D gaussian

which has radial symmetry: the probability that you end up in a certain small region depends only on how far you are from the origin, in the *euclidean* metric. this is despite the fact that the random walk itself is only defined knowing what up, down, left, and right are

@manylooseends

Hmm. So in what sense is the EM *reproduced*? I don’t think I see what exactly is reproducing it?

1:38 AM · Sep 20, 2020Twitter for iPad

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and

in the negative log probability. you need to take a particular scaling limit to see it come out and the details are slightly annoying to write down unfortunately

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and

Hmm yeah I think I need to do some more probability before understanding what you mean entirely haha. Love these kinds of discoveries in maths though. How’d you end up applying CLT to a random walk on a grid?