Multi-particle eccentricities in collisions dominated by fluctuations

We compute analytically the multi-particle eccentricities, ϵm{2n}ϵm{2n}, for systems dominated by fluctuations, such as proton–nucleus collisions at the Large Hadron Collider. In particular, we derive a general relation for 〈ϵ22n〉. We further discuss the relations between various multi-particle eccentricities and demonstrate that ϵ2{2}>ϵ2{4}≃ϵ2{6}≃ϵ2{8}ϵ2{2}>ϵ2{4}≃ϵ2{6}≃ϵ2{8}, in agreement with recent numerical calculations in a Glauber model.