Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A phase transition for non-intersecting Brownian motions, and the
  Painleve II equation   We consider n non-intersecting Brownian motions with two fixed starting
positions and two fixed ending positions in the large n limit. We show that in
case of 'large separation' between the endpoints, the particles are
asymptotically distributed in two separate groups, with no interaction between
them, as one would intuitively expect. We give a rigorous proof using the
Riemann-Hilbert formalism. In the case of 'critical separation' between the
endpoints we are led to a model Riemann-Hilbert problem associated to the
Hastings-McLeod solution of the Painleve II equation. We show that the Painleve
II equation also appears in the large n asymptotics of the recurrence
coefficients of the multiple Hermite polynomials that are associated with the
Riemann-Hilbert problem.

29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess