Abstract
The notion of a “deterministic equivalent” for random matrices, which can be found in the engineering literature, is a non-rigorous concept which amounts to replacing a random matrix model of finite size (which is usually unsolvable) by another problem which is solvable, in such a way that, for large N, the distributions of both problems are close to each other. Motivated by our example in the last chapter, we will in this chapter propose a rigorous definition for this concept, which relies on asymptotic freeness results. This “free deterministic equivalent” was introduced by Speicher and Vargas in [166].
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Mingo, J.A., Speicher, R. (2017). Deterministic Equivalents, Polynomials in Free Variables, and Analytic Theory of Operator-Valued Convolution. In: Free Probability and Random Matrices. Fields Institute Monographs, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6942-5_10
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DOI: https://doi.org/10.1007/978-1-4939-6942-5_10
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