Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random matrices and the average topology of the intersection of two
  quadrics   Let X_R be the zero locus in RP^n of one or two independently and Weyl
distributed random real quadratic forms (this is the same as requiring that the
corresponding symmetric matrices are in the Gaussian Orthogonal Ensemble). We
prove that the sum of the Betti numbers of X_R behaves asymptotically as n
(when n goes to infinity). The methods we use combine Random Matrix Theory,
Integral geometry and spectral sequences.

17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an