2007/02/12 by Øyvind Ryan, Ryan, Øyvind, Debbah, Mérouane · 1 citation
Mathematics · Physics and Astronomy · #15A52 (Secondary) #60F99 (Primary) 60C05 #FOS: Mathematics #Probability (math.PR) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.math/0702342
openalex publication_date 2007/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue distributions of random matrices will be strengthened further in this paper. It will be shown how the concept of multiplicative free convolution can be used to express known results for eigenvalue distributions of a type of random matrices called Information-Plus-Noise matrices. The result is proved in a free probability framework, and some new results, useful for problems related to free probability, are presented in this context. The connection between free probability and estimators for covariance matrices is also made through the notion of free deconvolution.