Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Gaussian random matrices determine the stability of Lotka-Volterra
  communities   The eigenvalue spectrum of a random matrix often only depends on the first
and second moments of its elements, but not on the specific distribution from
which they are drawn. The validity of this universality principle is often
assumed without proof in applications. In this letter, we offer a pertinent
counterexample in the context of the generalised Lotka-Volterra equations.
Using dynamic mean-field theory, we derive the statistics of the interactions
between species in an evolved ecological community. We then show that the full
statistics of these interactions, beyond those of a Gaussian ensemble, are
required to correctly predict the eigenvalue spectrum and therefore stability.
Consequently, the universality principle fails in this system. Our findings
connect two previously disparate ways of modelling complex ecosystems: Robert
May's random matrix approach and the generalised Lotka-Volterra equations. We
show that the eigenvalue spectra of random matrices can be used to deduce the
stability of dynamically constructed (or `feasible') communities, but only if
the emergent non-Gaussian statistics of the interactions between species are
taken into account.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn