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doi:10.22028/D291-30667
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: | https://www.degruyter.com/view/journals/crll/2017/732/article-p21.xml |
Link to this record: | hdl:20.500.11880/28961 http://dx.doi.org/10.22028/D291-30667 |
ISSN: | 0075-4102 1435-5345 |
Date of registration: | 6-Apr-2020 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Professorship: | MI - Prof. Dr. Roland Speicher |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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