Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling limit of the path leading to the leftmost particle in a
  branching random walk   We consider a discrete-time branching random walk defined on the real line,
which is assumed to be supercritical and in the boundary case. It is known that
its leftmost position of the $n$-th generation behaves asymptotically like
$\frac{3}{2}\ln n$, provided the non-extinction of the system. The main goal of
this paper, is to prove that the path from the root to the leftmost particle,
after a suitable normalizatoin, converges weakly to a Brownian excursion in
$D([0,1],\r)$.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics