Matrix Addition and the Dunkl Transform at High Temperature

We develop a framework for establishing the Law of Large Numbers eigenvalues in random matrix ensembles as size goes to infinity simultaneously with beta (inverse temperature) parameter going zero. Our approach is based on analysis (symmetric) Dunkl transform this regime. As an application we obtain LLN sums matrices inverse temperature 0. This results one-parameter family binary operations which interpolates between classical and free convolutions probability measures. also introduce study deformed cumulants, linearize operation.