Imagine a matrix filled with random numbers. At first glance, this chaos may look meaningless but what if there are predictable patterns hidden within this randomness? This is the central question of Random Matrix Theory (RMT), a field that studies the statistical properties of large random matrices.

On its own, a single random matrix might not reveal much, but when studied as part of an ensemble, its eigenvalue distribution and spacing distribution reveal universal patterns. This means the patterns don't depend on the fine-grained details of the randomness. It doesn't matter whether the entries came from a Gaussian distribution or a simple coin toss experiment the universal distribution remains unchanged. Wigner semicircle law and Marčenko–Pastur distributions are two of the most famous results of RMT that provide a theoretical baseline for what 'pure randomness' looks like. 

To be continued....