Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free Deterministic Equivalents, Rectangular Random Matrix Models, and
  Operator-Valued Free Probability Theory   Motivated by the asymptotic collective behavior of random and deterministic
matrices, we propose an approximation (called "free deterministic equivalent")
to quite general random matrix models, by replacing the matrices with operators
satisfying certain freeness relations. We comment on the relation between our
free deterministic equivalent and deterministic equivalents considered in the
engineering literature. We do not only consider the case of square matrices,
but also show how rectangular matrices can be treated. Furthermore, we
emphasize how operator-valued free probability techniques can be used to solve
our free deterministic equivalents.
  As an illustration of our methods we consider a random matrix model studied
first by R. Couillet, J. Hoydis, and M. Debbah. We show how its free
deterministic equivalent can be treated and we thus recover in a conceptual way
their result.
  On a technical level, we generalize a result from scalar valued free
probability, by showing that randomly rotated deterministic matrices of
different sizes are asymptotically free from deterministic rectangular
matrices, with amalgamation over a certain algebra of projections.
  In the Appendix, we show how estimates for differences between Cauchy
transforms can be extended from a neighborhood of infinity to a region close to
the real axis. This is of some relevance if one wants to compare the original
random matrix problem with its free deterministic equivalent.

5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th