Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rectangular random matrices, related free entropy and free Fisher's
  information   We prove that independent rectangular random matrices, when embedded in a
space of larger square matrices, are asymptotically free with amalgamation over
a commutative finite dimensional subalgebra $D$ (under an hypothesis of unitary
invariance). Then we consider elements of a finite von Neumann algebra
containing $D$, which have kernel and range projection in $D$. We associate
them a free entropy with the microstates approach, and a free Fisher's
information with the conjugate variables approach. Both give rise to
optimization problems whose solutions involve freeness with amalgamation over
$D$. It could be a first proposition for the study of operators between
different Hilbert spaces with the tools of free probability. As an application,
we prove a result of freeness with amalgamation between the two parts of the
polar decomposition of $R$-diagonal elements with non trivial kernel.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn