Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A random matrix approach to absorption in free products   This paper gives a free entropy theoretic perspective on amenable absorption
results for free products of tracial von Neumann algebras. In particular, we
give the first free entropy proof of Popa's famous result that the generator
MASA in a free group factor is maximal amenable, and we partially recover
Houdayer's results on amenable absorption and Gamma stability. Moreover, we
give a unified approach to all these results using $1$-bounded entropy. We show
that if $\mathcal{M} = \mathcal{P} * \mathcal{Q}$, then $\mathcal{P}$ absorbs
any subalgebra of $\mathcal{M}$ that intersects it diffusely and that has
$1$-bounded entropy zero (which includes amenable and property Gamma algebras
as well as many others). In fact, for a subalgebra $\mathcal{P} \leq
\mathcal{M}$ to have this absorption property, it suffices for $\mathcal{M}$ to
admit random matrix models that have exponential concentration of measure and
that "simulate" the conditional expectation onto $\mathcal{P}$.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th