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  "body": "\n## Summary\n\nA random matrix is a matrix whose entries are [[random variables|0PNRKMRC55]] on a common probability space.\nRandom matrix theory studies the laws of its [[eigenvalues|0BQAA2BK3Q]] and singular values, mostly when the size of the matrix grows.\nFor a large symmetric matrix with independent centred entries of equal variance, the scaled eigenvalues follow the [[Wigner semicircle distribution|3QTT95DMFH]].\nRandom matrices are used in nuclear physics, multivariate statistics, number theory and wireless communication.\n\n## Explanations\n\n### L1 human\n\nFill a square table with numbers drawn at random, for example by coin tosses or from a normal distribution.\nThe result is a random matrix, and its eigenvalues are random numbers too.\nFor one small matrix the eigenvalues look erratic.\nFor a large symmetric matrix with independent entries of mean $0$ and equal variance, a histogram of the eigenvalues, after scaling, has an almost fixed shape: a half circle.\nThis shows that randomness at the level of entries can create order at the level of the spectrum.\n",
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