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In this paper, we study propagation of chaos for the parabolic-parabolicKeller-Segel model with a logarithmic cut-off by establishing a rigorousconvergence analysis from a stochastic particle system to theparabolic-parabolic Keller-Segel (KS) equation for any dimension case. Underthe assumption that the initial data are independent and identicallydistributed (i.i.d.) with a common probability density function $\rho_0$, werigorously prove the propagation of chaos for this interacting system with acut-off parameter $\varepsilon\sim (\ln N)^{-\frac{2}{d+2}}$: when$N\rightarrow \infty$, the joint distribution of the particle system is$f$-chaotic and the measure $f$ possesses a density which is a weak solution tothe mean-field parabolic-parabolic KS equation.

Mean-field limit of a particle approximation for the parabolic-parabolic Keller-Segel model