Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonals of real symmetric matrices of given spectra as a measure space   The set of diagonals of real symmetric matrices of given non negative
spectrum is endowed with a measure which is obtained by the push forward of the
Haar measure of the real orthogonal group.\\ We prove that the Radon Nicodym
derivation of this measure with respect to the relative Euclidean measure is
approximated by the coefficients of a sequence of zonal sphere polynomials
corresponding with the given spectrum.
  There is a striking similarity between the role of the zonal sphere
polynomials in the orthogonal case, and that of the Schur function in the
Hermitian case.\\ Following this we obtain a combinatorial approximation for
the probability of real symmetric matrix of a given spectrum to appear as the
sum of two real symmetric matrices, each of a given spectrum. In addition we
obtain a real orthogonal analogue to the Zuber Itzykson Harish Chandra
integration formula.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph