On the applicability of Benjamini-Hochberg If I've understood correctly, the Benjamini-Hochberg (BH) correction is used to correct for the rate of false discoveries (FDR) when testing a collection of $m$ random variables, $\{X_1, \ldots,X_m\}$ against $m$ null hypotheses $\{H_0^1, \ldots, H_0^m\}$, of which $k\leq m$ can be true.
Now consider a situation where you have a set of random variables that are sorted. For example, $\{Y_1,\ldots,Y_m\}$ with $Y_m\leq\ldots \leq Y_1$ and each $Y_i\sim F_i$ (i.e., distributed according to $F_i$). An example of such a scenario would be the eigenvalues of a random matrix. Suppose now, that given a single null hypothesis $H_0$, and test statistic $T_i$, the $Y_i$'s are tested in descending order — i.e., $Y_1$, then $Y_2$, and so on, until $H_0$ is false. 
Is the BH correction also applicable here or is it a fundamentally different scenario? Or does the question of controlling FDR not arise at all?
 A: Instead of independent tests you have dependent tests.  But multiple testing concepts like familywise error rate (FWER) and false discovery rate (FDR) still apply.  The complication is in the computation of quantities like FWER as probabilities simultaneously rejecting two of the hypotheses is no longer the product of the individual rejection probabilities.
A: Sorted test statistics are not a problem for B-H as the (re)sorting is an inherent part of the procedure. 
In the eigenvalue case-- when testing for the rank of the eigenspace--  it is actually the dependence between the eigenvalues that is more problematic. I am not sure if the PRDS condition needed for B-H is satisfied, so you could either consider a more general FDR controlling procedure such as B-H-Y, or have a look at some works on the distribution of eigen values (say, B. Nadler and I.M. Johnstone Detection Performance of Roy's Largest Root Test when the noise covariance matrix is arbitrary, Statistical Signal Processing Conference, Nice, France, 2011.). 
