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  "body": "\n## Summary\n\nA [[measure-preserving transformation|556WBDAHNP]] is weakly mixing when the correlations $\\mu(T^{-n}A \\cap B) - \\mu(A)\\mu(B)$ tend to $0$ on average over $n$, in absolute value.\nIt sits strictly between [[mixing|S3RJQ9CX2P]] and [[ergodicity|AZRPHS478B]].\nWeak mixing has a clean spectral meaning: the [[Koopman operator|37TRG5DBQC]] has no eigenfunctions other than the constants.\nIt describes a system with no rotation hidden inside it.\n\n## Explanations\n\n### L1 human\n\nA weakly mixing system mixes sets together at almost all times, though it may fail to mix at some rare times.\nThe rare bad times have zero density among all times.\nRotations of a circle are not weakly mixing: they turn the space rigidly, and the function $e^{2\\pi i x}$ just gets multiplied by a constant at each step.\nWeak mixing says that no function on the space behaves in this rigid, periodic way.\n",
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