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  "body": "\n## Summary\n\nA probability distribution is infinitely divisible if, for every $n$, it is the law of a sum of $n$ [[independent and identically distributed|00MRN0FARV]] random variables.\nThe [[normal|05AQE0QR0D]], [[Poisson|0XB9GQTN9G]], [[gamma|0B80PAQD3C]] and [[Cauchy|0GPG24Q3GR]] laws are infinitely divisible, while no nondegenerate bounded law is.\nInfinitely divisible laws are exactly the laws at time $1$ of [[Lévy processes|8NT5CFG2ZR]], and they are described by the [[Lévy–Khintchine representation|Q82B4H4Z4J]].\nThey are also the possible limits of sums of many small independent terms.\n\n## Explanations\n\n### L1 human\n\nA law is infinitely divisible if it can be split into any number of equal independent parts.\nSuppose the number of calls to a call centre in one hour is Poisson with mean $60$.\nIt is the sum of the calls in $60$ independent minutes, each Poisson with mean $1$.\nIt is also the sum over $3600$ independent seconds, each Poisson with mean $1/60$.\nThis works for every number of parts, so the Poisson law is infinitely divisible.\nA fair coin with values $0$ and $1$ cannot be split even into two equal independent parts.\n",
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