# Tag Info

### Expectation of top-K selection of squared Gaussian random variables

Let $Z \sim \mathcal{N}(0,\sigma^2 I_n)$ be an $n$-dimensional Gaussian vector with independent $\mathcal{N}(0,\sigma^2)$ components. Consider the family of binary vectors in $\mathbb{R}^n$ with ...
• 146
1 vote

### $n$-wise extension of covariance / correlation

If you denote random variables by capital $X\text{s},$ you should stick with that, and probably reserve the lower-case $x$ for arguments to its p.d.f. and c.d.f. and the like. There is the idea of the ...
• 11.8k
1 vote

### $n$-wise extension of covariance / correlation

$\newcommand\Var{\operatorname{Var}}\newcommand\Cov{\operatorname{Cov}}$In conditions 1--3 in your post, the $x_i$'s are used improperly in place of the $X_i$'s. Also, the functions $C$ must of course ...
• 115k

### Points based partial ranking

This is an interesting question. An expert in social choice would have an interesting reply. As a semi-expert I can say semi-interesting things. As you may know, a common voting setting in social ...
• 4,429
Accepted

• 6,674
1 vote

### Relationship between fixed points and inversions in permutations

A counterexample for $n = 4$ was given in the comments (2431, per @PeterTaylor). Monte Carlo simulation results of my own suggest counterexamples ought to increase with increasing $n$. Moreover, the ...
• 173
Accepted

### Evolution of the empirical mean of a list as we remove elements proportional to their value

A simple mean field calculation suggests to look at the solution to $$\partial_t Q_t(k) = -\frac{k Q_t(k)}{\sum_\ell \ell Q_t(\ell)},\qquad Q_0 = P.$$ For all $n$, one would then expect a good ...
• 8,854
1 vote

### Evolution of the empirical mean of a list as we remove elements proportional to their value

I doubt this is an easy analysis, as the result is going to be affected by the distribution used for $P(k)$. I doubt there is a general form, but empirically there may be a well-behaved example. In ...
• 830