Matrix Addition and the Dunkl Transform at High Temperature

@article{BenaychGeorges2022MatrixAA,
  title={Matrix Addition and the Dunkl Transform at High Temperature},
  author={Florent Benaych-Georges and Cesar Cuenca and Vadim Gorin},
  journal={Communications in Mathematical Physics},
  year={2022}
}
We develop a framework for establishing the Law of Large Numbers for the eigenvalues in the random matrix ensembles as the size of the matrix goes to infinity simultaneously with the beta (inverse temperature) parameter going to zero. Our approach is based on the analysis of the (symmetric) Dunkl transform in this regime. As an application we obtain the LLN for the sums of random matrices as the inverse temperature goes to 0. This results in a one-parameter family of binary operations which… 
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