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We use a recently derived diagrammatic formulation of the dynamics ofinteracting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)]to study a four-point dynamic density correlation function. We re-sum a classof diagrams which separate into two disconnected components upon cutting asingle propagator. The resulting formula for the four-point correlationfunction can be expressed in terms of three-point functions closely related tothe three-point susceptibility introduced by Biroli et al. [Phys. Rev. Lett.97, 195701 (2006)] and the standard two-point correlation function. Thefour-point function has a structure very similar to that proposed by Berthierand collaborators [Science 310, 1797 (2005), J. Chem. Phys. 126, 184503(2007)]. It exhibits a small wave vector divergence at the mode-couplingtransition.

Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach