Marchenko-Pastur Law

The Marchenko-Pastur Law describes the distribution of eigenvalues of large random matrices, particularly in fields like statistics and finance. When you analyze the behavior of large datasets, this law predicts how the eigenvalues (which represent variances in data) are likely to distribute themselves. Specifically, it outlines a "bulk" region where most eigenvalues will fall, providing a benchmark for identifying unusual data patterns or structures. This has practical implications for understanding correlations in complex systems, such as networks or financial markets, helping analysts and researchers make sense of vast amounts of data.