  We compute analytically the multi-particle eccentricities, \epsilon_m {2n},
for systems dominated by fluctuations, such as proton-nucleus collisions at the
Large Hadron Collider. In particular, we derive a general relation for
<\epsilon_2^{2n}>. We further discuss the relations between various
multi-particle eccentricities and demonstrate that \epsilon_2{2} >
\epsilon_2{4} \simeq \epsilon_2{6} \simeq \epsilon_2{8}, in agreement with
recent numerical calculations in a Glauber model.
