Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinantal process starting from an orthogonal symmetry is a Pfaffian
  process   When the number of particles $N$ is finite, the noncolliding Brownian motion
(BM) and the noncolliding squared Bessel process with index $\nu > -1$
(BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial
configurations. In the present paper we prove that, if initial configurations
are distributed with orthogonal symmetry, they are Pfaffian processes in the
sense that any multitime correlation functions are expressed by Pfaffians. The
$2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians
processes are explicitly obtained by the equivalence between the noncolliding
BM and an appropriate dilatation of a time reversal of the temporally
inhomogeneous version of noncolliding BM with finite duration in which all
particles start from the origin, $N \delta_0$, and by the equivalence between
the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared
generalized meander starting from $N \delta_0$.

0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org