Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unified approach for large deviations of bulk and extreme eigenvalues
  of the Wishart ensemble   Within the framework of the Coulomb fluid picture, we present a unified
approach to derive the large deviations of bulk and extreme eigenvalues of
large Wishart matrices. By analysing the statistics of the shifted index number
we are able to derive a rate function $\Psi (c, x)$ depending on two variables:
the fraction $c$ of eigenvalues to the left of an infinite energetic barrier at
position $x$. For a fixed value of $c$, the rate function gives the large
deviations of the bulk eigenvalues. In particular, in the limits $c\to 0$ or
$c\to 1$ it is possible to extract the left and right deviations of the
smallest and largest eigenvalues, respectively. Alternatively, for a fixed
value $x$ of the barrier, the rate function provides the large deviations of
the shifted index number. All our analytical findings are compared with
Metropolis Monte Carlo simulations, obtaining excellent agreement.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph