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We provide a rigorous derivation of Einstein's formula for the effectiveviscosity of dilute suspensions of $n$ rigid balls, $n \gg 1$, set in a volumeof size $1$. So far, most justifications were carried under a strong assumptionon the minimal distance between the balls: $d_{min} \ge c n^{-\frac{1}{3}}$, $c> 0$. We relax this assumption into a set of two much weaker conditions: oneexpresses essentially that the balls do not overlap, while the other one givesa control of the number of balls that are close to one another. In particular,our analysis covers the case of suspensions modelled by standard Poissonprocesses with almost minimal hardcore condition.

Mild assumptions for the derivation of Einstein's effective viscosity formula