Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graph-based equilibrium problem for the limiting distribution of
  non-intersecting Brownian motions at low temperature   We consider n non-intersecting Brownian motion paths with p prescribed
starting positions at time t=0 and q prescribed ending positions at time t=1.
The positions of the paths at any intermediate time are a determinantal point
process, which in the case p=1 is equivalent to the eigenvalue distribution of
a random matrix from the Gaussian unitary ensemble with external source. For
general p and q, we show that if a temperature parameter is sufficiently small,
then the distribution of the Brownian paths is characterized in the large n
limit by a vector equilibrium problem with an interaction matrix that is based
on a bipartite planar graph. Our proof is based on a steepest descent analysis
of an associated (p+q) by (p+q) matrix valued Riemann-Hilbert problem whose
solution is built out of multiple orthogonal polynomials. A new feature of the
steepest descent analysis is a systematic opening of a large number of global
lenses.

6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex