  Relay (or remote) synchronization between two not directly connected
oscillators in a network is an important feature allowing distant coordination.
In this work, we report a systematic study of this phenomenon in multiplex
networks, where inter-layer synchronization occurs between distant layers
mediated by a relay layer that acts as a transmitter. We show that this
transmission can be extended to higher order relay configurations, provided
symmetry conditions are preserved. By first order perturbative analysis, we
identify the dynamical and topological dependencies of relay synchronization in
a multiplex. We find that the relay synchronization threshold is considerably
reduced in a multiplex configuration, and that such synchronous state is mostly
supported by the lower degree nodes of the outer layers, while hubs can be
de-multiplexed without affecting overall coherence. Finally, we experimentally
validated the analytical and numerical findings by means of a multiplex of
three layers of electronic circuits.the analytical and numerical findings by
means of a multiplex of three layers of electronic circuits.
