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Multi-particle eccentricities in collisions dominated by fluctuations

We compute analytically the multi-particle eccentricities, ε_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 <ε_2^{2n}>. We further discuss the relations between various multi-particle eccentricities and demonstrate that ε_2{2} > ε_2{4} \simeq ε_2{6} \simeq ε_2{8}, in agreement with recent numerical calculations in a Glauber model.