Free semicircular law

The free semicircular law is a concept from free probability theory that describes how the eigenvalues (special values associated with matrices) of large, random matrices behave. As the size of these matrices increases, the distribution of their eigenvalues tends to follow a specific shape called the semicircle law, which looks like a semi-elliptical curve. "Free" refers to a type of independence in this mathematical context, similar to independence in probability but for non-commuting variables. Essentially, the free semicircular law provides a predictable pattern for the spectral distribution of large complex systems represented by matrices.