  In this paper, we consider a hybrid millimeter wave (mmWave) and micro wave
($\mu$Wave) network from the perspective of \emph{wireless caching} and study
the optimal probabilistic content/file caching placement at desirable base
stations (BSs) using a stochastic geometric framework. Considering the average
success probability (ASP) of file delivery as the performance metric, we derive
expressions for the association probability of the typical user to the mmWave
and $\mu$Wave networks. Accordingly, we provide an upper bound for the ASP of
file delivery and formulate the content caching placement scheme as an
optimization problem with respect to caching probabilities, that jointly
optimizes the ASP of file delivery considering both content placement and
delivery phases. In particular, we consider the caching placement strategy
under both noise-limited and interference-limited environments. We numerically
evaluate the performance of the proposed caching schemes under essential
factors, such as blockages in the mmWave network, cluster radius, BS density,
and path loss and compare it with uniform caching placement, caching $M$ most
popular contents, and random caching placement. Numerical results demonstrate
the superiority of the proposed caching scheme over others, albeit certain
trade-offs.
