Let $X_1, \dots, X_n \sim_{iid} \chi^2_{m}$ be a random sample from a chi-squared distribution with $m$ degrees of freedom (d.f.). I was wondering if there's any known result for the order statistics

$$\max_{1 \le i \le n} X_i, \min_{1 \le i \le n} X_i $$

respectively as a function of $m$ and also $n$?

And finally, is there any known result for the ratio of this two order statistics:

$$ \frac{\max_{1 \le i \le n} X_i}{\min_{1 \le i \le n} X_i }?$$

P.S. I'm primarily interested **how these three quantities above behave w.r.t. increasing d.f. $m$ and w.r.t. increasing sample size $n$.**

In this regard, I've looked into this question on stats.SE, but couldn't make it helpful.

*Any references would also be appreciated.*