Clement C.'s user avatar
Clement C.'s user avatar
Clement C.'s user avatar
Clement C.
  • Member for 10 years, 11 months
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59 votes
11 answers
4k views

Striking applications of linearity of expectation

37 votes
1 answer
2k views

Application of Rolle's theorem? Establish existence of $c\in(a,b)$ such that $f(c)+f'(c)=f(c)f'(c)$

18 votes
9 answers
988 views

(Elegant) proof of : $x \log_2\frac{1}{x}+(1-x) \log_2\frac{1}{1-x} \geq 1- (1-\frac{x}{1-x})^2$

12 votes
2 answers
2k views

An inequality $ k\frac{\sum_{i\neq j} x_i x_j ( (1-x_i-x_j)^{k-1}- (1-x_i)^k(1-x_j)^k)}{\sum_{i=1}^n x_i (1-(1-x_i)^k)} \leq 2$

11 votes
0 answers
338 views

Name of a quantity related to Shannon entropy, but with squared logarithm

11 votes
3 answers
271 views

Limit of the sequence $\left(\sum_{k=0}^n f\!\left(\frac{k}{n^2}\right)\right)_n$.

11 votes
2 answers
2k views

Taylor series (or equivalent at $\epsilon\to0$) of the integral over $x$ of a function of $x$ and $\epsilon$

10 votes
2 answers
719 views

The case for L'Hôpital's rule?

8 votes
0 answers
1k views

Reference for the Gibbs variational principle/dual characterization of KL

8 votes
2 answers
842 views

Dominance Poisson/Binomial in convex order

8 votes
1 answer
476 views

Subgaussian tail bounds for maximum of subgaussian random variables: concentration around the true expectation?

7 votes
2 answers
392 views

Maximizing the ratio $\|p\|_\infty/\|p\|_2^2$ for a probability distribution $p$ on $n$ elements

7 votes
2 answers
2k views

A reference for a Gaussian inequality ($\mathbb{E} \max_i X_i$)

6 votes
1 answer
3k views

Sequence of continuous function converging pointwise to Thomae's function

6 votes
0 answers
199 views

Relating primal and dual characterization of an (interpolation) norm on $\ell_1+\ell_2$

6 votes
0 answers
268 views

$K$-functional between $\ell_1$ and $\ell_2$ for a specific sequence

6 votes
1 answer
655 views

Bhatia—Davis inequality: first recorded occurrence?

6 votes
1 answer
203 views

"Bernstein version" of McDiarmid?

6 votes
1 answer
338 views

Inequality $(\int_0^1 |f|)^2 \leq \frac{1}{12}\int_0^1 {f'}^2$

6 votes
1 answer
713 views

Differentiation and asymptotic equivalents.

5 votes
0 answers
201 views

Characterization of log-concavity based on the MGF or characteristic function?

5 votes
2 answers
253 views

"Elegant" proof that $f(x) \geq g(x)$

5 votes
2 answers
399 views

Basic question on Bregman divergences and strong convexity

5 votes
1 answer
201 views

Series expansion of $\sum_{k=1}^{n} \frac{\ln(k+1)}{k}$ to order $o(1)$

4 votes
2 answers
409 views

Minimizing the expectation over a set, wrt to the Gaussian measure

4 votes
0 answers
276 views

Finding a hidden "heavy" subset of random variables.

4 votes
1 answer
200 views

If $h$ is closer to $f$ than to $g$, its integral on $\{f > g\}$ must "agree" with $f$'s?

4 votes
0 answers
232 views

Decrease of $L_1$ norm of piecewise constant functions after some "averaging"

4 votes
2 answers
161 views

What is the simplest way to obtain asymptotics of $\sum_{k=0}^n \binom{n}{k} \frac{1}{(1+k)^2}$?

3 votes
1 answer
83 views

Is it true that $\mathbb{E}[| Z\rvert]+|\mathbb{E}[Z]\rvert\geq\mathbb{E}[|\mathbb{E}[Z\mid X]\rvert]+\mathbb{E}[|\mathbb{E}[Z\mid Y]\rvert]$?