List questions from probability-limit-theorems

Published on 26 Mar 2026 - 4:14

234

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Convergence in Kolmogorov distance

Published on 07 Mar 2022 - 18:34

37

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Asymptotic convergence of shifted and scaled Wigner matrix

Published on 30 Mar 2026 - 0:21

73

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Generalization of central limit theorem to sums of the form $\sum_{k=1}^n\frac{1}{X_k^m}$, $m=1,2,\dots$?

Published on 26 Mar 2026 - 14:34

30

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Big $\mathcal{O}$ of a Tuple

Published on 22 Mar 2022 - 21:05

128

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If $X_n \overset{\text{a.s.}}{\to} \infty$ and $Y_n = O_P(1)$, does $X_n + Y_n \to \infty$ in probability or almost surely?

Published on 23 Mar 2022 - 14:15

47

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Why is $\frac{1}{n} \sup_{k\le n} |T_k - k| \to_{a.s.} 0$ if $T_n/n \to E T_1 = 1$?

Published on 23 Mar 2022 - 22:20

284

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The order statistics of uniform distribution $U_{n,k_n}\rightarrow p$ a.s., when $\frac{K_n}{n} \rightarrow p$

Published on 28 Mar 2022 - 10:39

271

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Durrett's Continuity Theorem Proof (Theorem 3.3.17)

Published on 30 Mar 2022 - 15:07

80

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The order statistics of uniform distribution $U_{n,{k_n}}$ times $n$ tends to $\infty$ in probability.

Published on 05 Apr 2022 - 15:44

44

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Estimate of Expectation of Estimated Function

Published on 30 Mar 2026 - 16:25

166

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Limit of expectation of maximum of standard normal distribution

Published on 25 Feb 2026 - 4:36

79

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Does a Gaussian random walk lead to a Gaussian distribution in the limit, even when the initial state is non-Gaussian?

Published on 25 Feb 2026 - 6:15

62

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Generalizing Bernoulli's theorem to any sequence of IID random variables

Published on 09 Apr 2022 - 22:16

27

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About minimum 2 and maximum 9 probability

Published on 13 Apr 2022 - 12:47

List Question

A new convergence problem for the conditional expectation

Convergence in Kolmogorov distance

Asymptotic convergence of shifted and scaled Wigner matrix

Generalization of central limit theorem to sums of the form $\sum_{k=1}^n\frac{1}{X_k^m}$, $m=1,2,\dots$?

Big $\mathcal{O}$ of a Tuple

If $X_n \overset{\text{a.s.}}{\to} \infty$ and $Y_n = O_P(1)$, does $X_n + Y_n \to \infty$ in probability or almost surely?

Why is $\frac{1}{n} \sup_{k\le n} |T_k - k| \to_{a.s.} 0$ if $T_n/n \to E T_1 = 1$?

The order statistics of uniform distribution $U_{n,k_n}\rightarrow p$ a.s., when $\frac{K_n}{n} \rightarrow p$

Durrett's Continuity Theorem Proof (Theorem 3.3.17)

The order statistics of uniform distribution $U_{n,{k_n}}$ times $n$ tends to $\infty$ in probability.

Estimate of Expectation of Estimated Function

Limit of expectation of maximum of standard normal distribution

Does a Gaussian random walk lead to a Gaussian distribution in the limit, even when the initial state is non-Gaussian?

Generalizing Bernoulli's theorem to any sequence of IID random variables

About minimum 2 and maximum 9 probability

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