Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global structure of semi-infinite geodesics and competition interfaces
  in Brownian last-passage percolation   In Brownian last-passage percolation (BLPP), the Busemann functions $\mathcal
B^{\theta}(\mathbf x,\mathbf y)$ are indexed by two points $\mathbf x,\mathbf y
\in \mathbb Z \times \mathbb R$, and a direction parameter $\theta > 0$. We
derive the joint distribution of Busemann functions across all directions. The
set of directions where the Busemann process is discontinuous, denoted
$\Theta$, provides detailed information about the uniqueness and coalescence of
semi-infinite geodesics. The uncountable set of initial points in BLPP gives
rise to new phenomena not seen in discrete models. For example, in every
direction $\theta > 0$, there exists a countably infinite set of initial points
$\mathbf x$ such that there exist two $\theta$-directed geodesics that split
but eventually coalesce. Further, we define the competition interface in BLPP
and show that the set of initial points whose competition interface is
nontrivial has Hausdorff dimension $\frac{1}{2}$. From each of these
exceptional points, there exists a random direction $\theta \in \Theta$ for
which there exists two $\theta$-directed semi-infinite geodesics that split
immediately and never meet again. Conversely, when $\theta \in \Theta$, from
every initial point $\mathbf x \in \mathbb Z \times \mathbb R$, there exists
two $\theta$-directed semi-infinite geodesics that eventually separate.
Whenever $\theta \notin \Theta$, all $\theta$-directed semi-infinite geodesics
coalesce.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph