Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Valence independent formula for the equilibrium measure   We derive a new formula for the equilibrium measure for eigenvalues of random
matrices sampled from polynomial perturbations of the GUE, valid in the one-cut
case. The virtue of our formula is that it depends on the potential only
implicitly through the endpoints of support of the equilibrium measure. Our
motivation is the problem of computing explicit formulas for generating
functions which enumerate graphs embedded in a Riemann surface. To demonstrate
the utility of our formula for the equilibrium measure, we derive a formula for
the generating function $e_1$ enumerating maps on the torus. This formula is
"valence independent" in the sense that it holds regardless of what numbers of
edges are allowed to meet at vertices; furthermore it subsumes formulas for
$e_1$ given by other authors as special cases.

32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an