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-3 votes
0 answers
134 views

Approximation on Dirichlet's arithmetic progression by means of central limit theorem

In this video lecture on Number theory over function fields taught by Will Sawin is presented a 'conceptional' reason for error estimation $\#\{p \in \Bbb P: p =a \ \text{mod} \ N, p <x \} =\frac{1}...
JackYo's user avatar
  • 619
6 votes
1 answer
374 views

Almost evenly distributed spherical random vectors

Consider $n$ i.i.d spherically distributed random vectors $z_1 ,\cdots , z_n \sim \text{Unif}(\mathbb{S}^{d-1})$. What is the best lower bound on $n$ for which whp there exists a constant $c>0$ ...
Sina Baghal's user avatar
15 votes
2 answers
10k views

Convergence of moments implies convergence to normal distribution

I have a sequence $\{X_n\}$ of random variables supported on the real line, as well as a normally distributed random variable $X$ (whose mean and variance are known but irrelevant). I know that the ...
Greg Martin's user avatar
  • 12.8k