Random Matrix Hypothesis

The Random Matrix Hypothesis suggests that in complex systems—like energy levels in heavy atoms or financial markets—certain patterns emerge that can be modeled using matrices filled with random numbers. Instead of trying to precisely predict each component, scientists analyze the overall statistical properties of these matrices. This approach helps identify universal behaviors and correlations, revealing underlying structures despite apparent randomness. Essentially, it treats complex, unpredictable systems as if they were governed by random matrices, which provides valuable insights into their collective behavior without requiring detailed, exact knowledge of every element.