  Unreliable fading wireless channels are the main challenge for strict
performance guarantees in mobile communications. Diversity schemes including
massive number of antennas, huge spectrum bands and multi-connectivity links
are applied to improve the outage performance. The success of these approaches
relies heavily on the joint distribution of the underlying fading channels. In
this work, we consider the $\varepsilon$-outage capacity of slowly fading
wireless diversity channels and provide lower and upper bounds for fixed
marginal distributions of the individual channels. This answers the question
about the best and worst case outage probability achievable over $n$ fading
channels with a given distribution, e.g., Rayleigh fading, but not necessarily
statistically independent. Interestingly, the best-case joint distribution
enables achieving a zero-outage capacity greater than zero without channel
state information at the transmitter for $n \geq 2$. Furthermore, the results
are applied to characterize the worst- and best-case joint distribution for
zero-outage capacity with perfect channel state information everywhere. All
results are specialized to Rayleigh fading and compared to the standard
assumption of independent and identically distributed fading component
channels. The results show a significant impact of the joint distribution and
the gap between worst- and best-case can be arbitrarily large.
