Free additive convolution

Free additive convolution is a concept from free probability theory that describes how the "spectral distributions" (eigenvalue patterns) of large, independent random matrices combine when added together. Unlike classical probability, where independent variables add their distributions directly, free additive convolution models the non-commutative, or matrix, case. It provides a mathematical way to predict the eigenvalue distribution of the sum of two large, independent random matrices, capturing their combined spectral behavior without needing their specific entries, just their individual spectral distributions.