Free Probability and Random Matrices

By Roland Speicher. 2014

220 citations recorded by the source corpus.

The concept of freeness was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices. We will show how the combination of various free probability results with a linearization trick allows to address successfully the problem of determining the asymptotic eigenvalue distribution of general selfadjoint polynomials in independent random matrices.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5e6554d3e1cced2b1e4c89e260af5cdcda77843d

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Eigenvalues of non-hermitian random matrices and Brown measure of non-normal operators: hermitian reduction and linearization method (2015, background): “It turns out that many classes of random matrices have a limit in a sense of ⋆–moments and the limit operator can be found by the means of free probability theory [41, 24, 28].”