= Kac chaos
{c}
{title2=$\Pi_k(F_N)\rightharpoonup f^{\otimes k}$}
A permutation-symmetric sequence of probability laws is chaotic with one-particle law $f$ when, for every fixed $k$, its $k$-coordinate <marginal distributions> converge weakly to the product law $f^{\otimes k}$ as $N\to\infty$. This is an asymptotic independence condition, not a consequence of symmetry alone. A rigorous kinetic limit also requires propagation of this property under the dynamics and sufficient convergence to pass collision <integrals>.
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