  The work establishes the exact performance limits of stochastic coded caching
when users share a bounded number of cache states, and when the association
between users and caches, is random. Under the premise that more balanced
user-to-cache associations perform better than unbalanced ones, our work
provides a statistical analysis of the average performance of such networks,
identifying in closed form, the exact optimal average delivery time. To
insightfully capture this delay, we derive easy to compute closed-form
analytical bounds that prove tight in the limit of a large number $\Lambda$ of
cache states. In the scenario where delivery involves $K$ users, we conclude
that the multiplicative performance deterioration due to randomness -- as
compared to the well-known deterministic uniform case -- can be unbounded and
can scale as $\Theta\left( \frac{\log \Lambda}{\log \log \Lambda} \right)$ at
$K=\Theta\left(\Lambda\right)$, and that this scaling vanishes when
$K=\Omega\left(\Lambda\log \Lambda\right)$. To alleviate this adverse effect of
cache-load imbalance, we consider various load balancing methods, and show that
employing proximity-bounded load balancing with an ability to choose from $h$
neighboring caches, the aforementioned scaling reduces to $\Theta
\left(\frac{\log(\Lambda / h)}{ \log \log(\Lambda / h)} \right)$, while when
the proximity constraint is removed, the scaling is of a much slower order
$\Theta \left( \log \log \Lambda \right)$. The above analysis is extensively
validated numerically.
