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

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

)

@QiaochuYuan

Sep 20, 2020

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

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

Replying to

and

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

6:34 PM · Sep 20, 2020Twitter for iPad

nilan is open for collaboration (46/100)

Replying to

and

what would be a nice proof sketch?

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

)

@QiaochuYuan

Sep 20, 2020

it follows from the central limit theorem but you can also give a more direct and maybe revealing proof by writing the relevant probabilities in terms of binomial coefficients and using stirling’s formula (which will essentially prove CLT for binomial distributions)