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Asymptotic behavior of functions, asymptotic series and related topics

21 votes
3 answers
2k views

Probability of two vectors lying in the same orthant

In particular, I am interested in the asymptotics of large $d \to \infty$ of $f_d(\theta)$ for $\theta \in (0, \frac{1}{2} \pi)$. …
TMM's user avatar
  • 733
8 votes
2 answers
3k views

Expectation of Maximum of Uniform Multinomial Distribution

Can we say anything about $\mathbb{E}(m)$, and in particular, its asymptotics as $n \to \infty$? … But I am interested in (exact) asymptotics for the mean, so such approximations don't seem very useful. …
TMM's user avatar
  • 733
9 votes
2 answers
1k views

Expected centered entropy of the binomial distribution

.$$ Note that the latter expression does not contain $n$ anymore; I am interested in large-$n$ asymptotics of $I_n(p)$ which leads to the above, $n$-independent expression. …
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  • 733