A random matrix is a matrix whose elements are randomly generated according to some probability distribution. Random matrices are a central object of study in various fields, including mathematics, statistics, physics, and engineering, and they are used to model complex systems and phenomena in these areas.
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A random matrix is a matrix whose entries are random variables. Its eigenvalues form a random configuration, and its empirical spectral measure records their distribution with equal mass on each eigenvalue. Entry assumptions and normalization determine the spectral regime.