Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional limit theorem for the sine-process   The main result of this paper is a functional limit theorem for the
sine-process. In particular, we study the limit distribution, in the space of
trajectories, for the number of particles in a growing interval. The
sine-process has the Kolmogorov property and satisfies the Central Limit
Theorem, but our functional limit theorem is very different from the Donsker
Invariance Principle. We show that the time integral of our process can be
approximated by the sum of a linear Gaussian process and independent Gaussian
fluctuations whose covariance matrix is computed explicitly. We interpret these
results in terms of the Gaussian Free Field convergence for the random matrix
models. The proof relies on a general form of the multidimensional Central
Limit Theorem under the sine-process for linear statistics of two types: those
having growing variance and those with bounded variance corresponding to
observables of Sobolev regularity $1/2$.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an