Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schwinger-Dyson and loop equations for a product of square Ginibre
  random matrices   In this paper, we study the product of two complex Ginibre matrices and the
loop equations satisfied by their resolvents (i.e. the Stieltjes transform of
the correlation functions). We obtain using Schwinger-Dyson equation (SDE)
techniques the general loop equations satisfied by the resolvents. In order to
deal with the product structure of the random matrix of interest, we consider
SDEs involving the integral of higher derivatives. One of the advantage of this
technique is that it bypasses the reformulation of the problem in terms of
singular values. As a byproduct of this study we obtain the large $N$ limit of
the Stieltjes transform of the $2$-point correlation function, as well as the
first correction to the Stieltjes transform of the density, giving us access to
corrections to the smoothed density. In order to pave the way for the
establishment of a topological recursion formula we also study the geometry of
the corresponding spectral curve. This paper also contains explicit results for
different resolvents and their corrections.

36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga