Conversation

Sep 19, 2020

i'm going to bed but let's try and set up a game 1. reply with an interest, a picture, a quote, whatever – something random that you'd like to talk about with someone. ask a question, state an observation 2. reply to someone else in the replies enjoy your new friends

128

QC (in Berlin 7/29-??? w/ COVID

)

@QiaochuYuan

Replying to

@visakanv

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

1:00 AM · Sep 20, 2020Twitter for iPad

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and

shortest distance between two points is a straight line

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and

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

QC (in Berlin 7/29-??? w/ COVID

)

@QiaochuYuan

Sep 20, 2020

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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and

I would like to hear more about it.

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and

random walks have a funny habit of introducing square roots

Emily

@the_aiju

Sep 20, 2020

have you discovered the satanic thing that is <delta(x)> yet

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Replying to

and

Care to share a link detailing the derivation? :-) And is what’s bothering you the loss of discreteness, and the emergence of homogeneity and isotropy? Could think of that as subleading/“irrelevant” operators decaying under RG flow from coarse graining.

Replying to

and

i don’t understand why you think it’s wrong — it does seem that it would be the case that with enough samples, there would be radial symmetry but perhaps you are asking about whether a meaningful proof exists?

QC (in Berlin 7/29-??? w/ COVID

)

@QiaochuYuan

Sep 20, 2020

oh that’s not what i mean by “wrong,” i know the result is correct and i can prove it a few different ways i mean like *morally* wrong lol, it was kind of a joke. the result is much nicer than it has any right to be and i don’t feel like i have a complete understanding of why

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and

There is only one way to reach [n, 0] from [0,0] in n steps but there are a lot more ways (n-1 if I'm counting correctly) to reach [n-1, 1] in n steps. And there's many more ways to reach [n-2, 2]. So the resulting shape can't be the square.