Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Test configurations, large deviations and geodesic rays on toric
  varieties   This article contains a detailed study, in the toric case, of the test
configuration geodesic rays defined by Phong-Sturm. We show that the `Bergman
approximations' of Phong-Sturm converge in C^1 to the geodesic ray and that the
geodesic ray itself is C^{1,1} and no better. The \kahler metrics associated to
the geodesic ray of potentials are discontinuous across certain hypersurfaces
and are degenerate on certain open sets. A novelty in the analysis is the
connection between Bergman metrics, Bergman kernels and the theory of large
deviations.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom