  The following anticoncentration property is proved. The probability that the
$k$-order statistic of an arbitrarily correlated jointly Gaussian random vector
$X$ with unit variance components lies within an interval of length
$\varepsilon$ is bounded above by $2{\varepsilon}k ({ 1+\mathrm{E}[\|X\|_\infty
]}) $. This bound has implications for generalized error rate control in
statistical high-dimensional multiple hypothesis testing problems, which are
discussed subsequently.
