Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomly coupled differential equations with elliptic correlations   We consider the long time asymptotic behavior of a large system of $N$ linear
differential equations with random coefficients. We allow for general elliptic
correlation structures among the coefficients, thus we substantially generalize
our previous work [14] that was restricted to the independent case. In
particular, we analyze a recent model in the theory of neural networks [27]
that specifically focused on the effect of the distributional asymmetry in the
random connectivity matrix $X$. We rigorously prove and slightly correct the
explicit formula from [28] on the time decay as a function of the asymmetry
parameter. Our main tool is an asymptotically precise formula for the
normalized trace of $f(X) g(X^*)$, in the large $N$ limit, where $f$ and $g$
are analytic functions.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con