  Relativistic magnetically dominated turbulence is an efficient engine for
particle acceleration in a collisionless plasma. Ultrarelativistic particles
accelerated by interactions with turbulent fluctuations form non-thermal
power-law distribution functions in the momentum (or energy) space,
$f(\gamma)d\gamma\propto \gamma^{-\alpha}d\gamma$, where $\gamma$ is the Lorenz
factor. We argue that in addition to exhibiting non-Gaussian distributions over
energies, particles energized by relativistic turbulence also become highly
intermittent in space. Based on particle-in-cell numerical simulations and
phenomenological modeling, we propose that the bulk plasma density has
log-normal statistics, while the density of the accelerated particles, $n$, has
a power-law distribution function, $P(n)dn\propto n^{-\beta}dn$. We argue that
the scaling exponents are related as $\beta\approx \alpha+1$, which is broadly
consistent with numerical simulations. Non-space-filling, intermittent
distributions of plasma density and energy fluctuations may have implications
for plasma heating and for radiation produced by relativistic turbulence.
