  In this work, we study a stochastic system of N particles associated with the
parabolic-parabolic Keller-Segel system. This particle system is singular and
non Markovian in that its drift term depends on the past of the particles. When
the sensitivity parameter is sufficiently small, we show that this particle
system indeed exists for any $N\geq 2$, we show tightness in $N$ of its
empirical measure, and that any weak limit point of this empirical measure, as
$N\to\infty$, solves some nonlinear martingale problem, which in particular
implies that its family of time-marginals solves the parabolic-parabolic
Keller-Segel system in some weak sense. The main argument of the proof consists
of a Markovianization of the interaction kernel: We show that, in some loose
sense, the two-by-two path-dependant interaction can be controlled by a
two-by-two Coulomb interaction, as in the parabolic-elliptic case.
