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
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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
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Is this one run showing intermediate steps? Or is this multiple runs of the simulation? Also what does the yellow mean?
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idk i just pulled the first image off google that looked right. i don’t know what the yellow means. i think this should be multiple runs and showing the final locations of the walks only. pictures of the walks themselves are also interesting but not what i’m getting at
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well x and y are independent, so we can think about the 1 dimensional case? and your end location doesn't depend on the order, just the final totals. so for Up and Down, ending up r from the origin, P(r) = P(U - D) = P(U) + P(-D), so CLT says r will be normal? is that what's 🤯?
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what’s mindblowing to me is that the 2D gaussian you get is radially symmetric even though the definition of the random walk itself isn’t. this is less clear in the picture than it could be; with more points it would be clearer that the contour lines are circles
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yeah it’s clear we don’t get squares and it’s maybe baffling that we get circles idk