List questions from asymptotics

Published on 07 Mar 2019 - 12:11

374

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Disprove Big-O statement

Published on 07 Mar 2019 - 20:04

74

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Are $\lim_{x \to \infty} \frac{\Psi(x)}{\pi(x)}=1$ and $\pi(x)\le\Psi(x)$ true statements?

Published on 27 Mar 2026 - 10:47

399

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Sum of functions is big Oh

Published on 27 Mar 2026 - 12:28

400

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If $X_i∼fλ$, $Z∼\mathcal N(0,I_d)$ and $Y=X+\ell d^{-α}Z$ with $α<1/2$, then $\liminf_{d→∞}\text E\left[1∧\prod_{i=1}^d\frac{f(Y_i)}{f(X_i)}\right]=0$

Published on 26 Mar 2026 - 8:55

29

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Does limiting iteration count when performing permutation on a set change the time complexity?

Published on 08 Mar 2019 - 15:17

58

Views

Deriving asymptotic expansion of $\int_{-1}^{1} e^{i\lambda(\frac{x^3}{3}+x)} dx$

Published on 09 Mar 2019 - 16:26

46

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Bounding sum (log factor)

Published on 29 Mar 2026 - 14:55

61

Views

Dynamical system - System of non-linear 1st order autonomous ODEs: future stability

Published on 26 Mar 2026 - 2:58

72

Views

Sudoku solution size

Published on 29 Mar 2026 - 19:28

1.8k

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Comparing the growth rate of two functions using L'Hopital's rule

Published on 10 Mar 2019 - 22:58

29

Views

Determining whether $g(n)$ is $O(f(n))$

Published on 11 Mar 2019 - 4:03

798

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Asymptotics for rapidly-oscillating integral with no stationary point of the phase

Published on 11 Mar 2019 - 14:11

89

Views

What values of $\alpha$, if any, yield $f = \mathcal{O}(\epsilon^\alpha)$ as $\epsilon\downarrow 0$?

Published on 27 Mar 2026 - 10:47

50

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Prove a sequence is a $O(1/n^3)$

Published on 13 Mar 2019 - 7:35

List Question

Difficulty understanding the following taylor expansion

Disprove Big-O statement

Are $\lim_{x \to \infty} \frac{\Psi(x)}{\pi(x)}=1$ and $\pi(x)\le\Psi(x)$ true statements?

Sum of functions is big Oh

If $X_i∼fλ$, $Z∼\mathcal N(0,I_d)$ and $Y=X+\ell d^{-α}Z$ with $α<1/2$, then $\liminf_{d→∞}\text E\left[1∧\prod_{i=1}^d\frac{f(Y_i)}{f(X_i)}\right]=0$

Does limiting iteration count when performing permutation on a set change the time complexity?

Deriving asymptotic expansion of $\int_{-1}^{1} e^{i\lambda(\frac{x^3}{3}+x)} dx$

Bounding sum (log factor)

Dynamical system - System of non-linear 1st order autonomous ODEs: future stability

Sudoku solution size

Comparing the growth rate of two functions using L'Hopital's rule

Determining whether $g(n)$ is $O(f(n))$

Asymptotics for rapidly-oscillating integral with no stationary point of the phase

What values of $\alpha$, if any, yield $f = \mathcal{O}(\epsilon^\alpha)$ as $\epsilon\downarrow 0$?

Prove a sequence is a $O(1/n^3)$

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