Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Deviation Principles via Spherical Integrals   In this article, we develop a framework to study the large deviation
principle for matrix models and their quantized versions, by tilting the
measures using the limits of spherical integrals obtained in [46,47]. As
examples, we obtain
  1. a large deviation principle for the empirical distribution of the diagonal
entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and
unitary Haar distributed matrices $U$;
  2. a large deviation upper bound for the empirical eigenvalue distribution of
$A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$,
and their complementary lower bounds at measures which are described by the
free product with amalgamation;
  3. a large deviation principle for the Kostka number $K_{\boldsymbol\lambda_N
\boldsymbol\eta_N}$, for two sequences of partitions $\boldsymbol\lambda_N,
\boldsymbol\eta_N$ with at most $N$ rows;
  4. a large deviation upper bound for the Littlewood-Richardson coefficients
$c_{\boldsymbol\lambda_N \boldsymbol \eta_N}^{\boldsymbol \kappa_N}$, for three
sequences of partitions $\boldsymbol\lambda_N, \boldsymbol \eta_N, \boldsymbol
\kappa_N$ with at most $N$ rows, and their complementary lower bounds at nice
measures.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc