Please use this identifier to cite or link to this item: doi:10.22028/D291-30667
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Title: Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem
Author(s): Belinschi, Serban T.
Mai, Tobias
Speicher, Roland
Language: English
Title: Journal für die reine und angewandte Mathematik
Volume: 2017
Issue: 732
Startpage: 21
Endpage: 53
Publisher/Platform: De Gruyter
Year of Publication: 2017
Publikation type: Journal Article
Abstract: 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 Fréchet 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: Let X(N)1,…,X(N)n be selfadjoint N×N random matrices which are, for N→∞, asymptotically free. Consider a selfadjoint polynomial p in n non-commuting variables and let P(N) be the element P(N)=p(X(N)1,…,X(N)n). How can we calculate the asymptotic eigenvalue distribution of P(N) out of the asymptotic eigenvalue distributions of X(N)1,…,X(N)n?
DOI of the first publication: 10.1515/crelle-2014-0138
URL of the first publication:
Link to this record: hdl:20.500.11880/28961
ISSN: 0075-4102
Date of registration: 6-Apr-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Prof. Dr. Roland Speicher
Collections:UniBib – Die Universitätsbibliographie

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