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  "body": "\n## Summary\n\nThe Tracy–Widom distributions are the limit laws of the largest eigenvalue of large random Hermitian or symmetric matrices, after centring and scaling.\nThere are three of them, $F_1$, $F_2$ and $F_4$, for the orthogonal, unitary and symplectic Gaussian ensembles.\nThey are given by a solution of the Painlevé II equation, or by a Fredholm determinant with the Airy kernel.\nThey also appear far from matrices, for example for the longest increasing subsequence of a random permutation and for random growth models.\n\n## Explanations\n\n### L1 human\n\nThe eigenvalues of a large random matrix fill an interval, by the [[semicircle law|3QTT95DMFH]].\nThe largest one sits near the right end of that interval, with small random fluctuations.\nAfter zooming in by the right factor, these fluctuations follow a fixed law, the Tracy–Widom law.\nIt is not the normal law: it is asymmetric, with a left tail and a right tail that decay at different speeds.\n",
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