Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem
By Serban Teodor Belinschi, Tobias Mai, Roland Speicher. 2013
134 citations recorded by the source corpus.
We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just given by power series expansions, but are defined as Frechet analytic functions in all of the operator upper half plane. Furthermore, we do not have to assume that our state is tracial. Combining this new analytic theory of operator-valued free convolution with Anderson's selfadjoint version of the linearization trick we are able to provide a solution to the following general random matrix problem: How can we calculate the asymptotic eigenvalue distribution of a polynomial evaluated in independent random matrices with known asymptotic eigenvalue distributions?
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/67d41652518461a50ef4a2d52ca2a9581a2e17d4
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In Applied Mathematics
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Free Probability and Random Matrices (2014, methodology): “Here is now the main theorem from [23] on operator-valued free additive convolution.”