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The exact boundary is not established.","posed_since":"2010","precise":"For particles in $d$ dimensions with pair potential $V(r) \\sim 1/r^{\\alpha}$, determine the range of $\\alpha$ for which the $N \\to \\infty$ dynamics follows a Vlasov equation with quasi-stationary states whose lifetime diverges with $N$, as opposed to collisional relaxation on $N$-independent times; the proposed criterion is $\\alpha < d - 1$ (force integrable at large distance). An answer is a classification with proof or with simulations controlling $N \\to \\infty$.","problem_ref":"3b1aa32af3486e7ba53b0a7f3b6cc59b97392913134703a17bedb01f3145575a","references":"","settled_by":"A kinetic-theory derivation of the $N$ dependence of relaxation times for general $\\alpha$, confirmed by simulations in $d = 1, 2, 3$.","status_note":"The criterion was proposed by Gabrielli, Joyce and Marcos (Phys. Rev. Lett. 105, 210602, 2010); a derivation for general $\\alpha$ and $d$ is incomplete.","title":"Which power-law decays make interactions dynamically 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