  Assume that $X$ and $Y$ are independent random variables, each having a
Cauchy distribution with a known median. Taking a random independent sample of
size $n$ of each $X$ and $Y$, one can then compute their centralized empirical
correlation coefficient $r$. Analytically investigating the sampling
distribution of this $r$ appears possible only in the large $n$ limit; this is
what we have done in this article, deriving several new and interesting
results.
