Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ewens measures on compact groups and hypergeometric kernels   On unitary compact groups the decomposition of a generic element into product
of reflections induces a decomposition of the characteristic polynomial into a
product of factors. When the group is equipped with the Haar probability
measure, these factors become independent random variables with explicit
distributions. Beyond the known results on the orthogonal and unitary groups
(O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family
of probability changes analogous to the biassing in the Ewens sampling formula
known for the symmetric group. Then we study the spectral properties of these
measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The
associated orthogonal polynomials give rise, as $n$ tends to infinity to a
limit kernel at the singularity.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph