Marchenko–Pastur theorem

The Marchenko–Pastur theorem describes the behavior of eigenvalues (a kind of mathematical measure) of large random matrices, particularly those built from many independent random variables. When the size of these matrices becomes very large, the distribution of their eigenvalues follows a predictable pattern called the Marchenko–Pastur distribution. This result is fundamental in fields like statistics and physics because it helps understand the typical spectral behavior of complex systems and data, especially in high-dimensional settings such as large dataset analysis or signal processing, where it aids in distinguishing meaningful signals from random noise.