We obtain the mean field limit and the propagation of chaos for a system of
particles interacting with a singular interaction force of the type
1/∣x∣α, with α<1 in dimension d≥3. We also provide
results for forces with singularity up to α<d−1 but with large enough
cut-off. This last result thus almost includes the most interesting case of
Coulombian or gravitational interaction, but it is also interesting when the
strength of the singularity α is larger but close to one, in which case
it allows for very small cut-off.Comment: 47 pages. This version: improvement of the presentation, in
particular of the deterministic result