Papers › Analytic subordination theory of operator-valued free additive convolution and the...

Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem

13 Mar 2013arXiv:1303.3196links table onlyarchive 2025-07-28

Serban Belinschi, Tobias Mai, Roland Speicher

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

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?

PaperPDFCode

Code

johannes-hoffmann/ncdist.jl mentioned on GitHub report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections