Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The oriented swap process   Particles labelled $1,...,n$ are initially arranged in increasing order.
Subsequently, each pair of neighboring particles that is currently in
increasing order swaps according to a Poisson process of rate 1. We analyze the
asymptotic behavior of this process as $n\to\infty$. We prove that the
space--time trajectories of individual particles converge (when suitably
scaled) to a certain family of random curves with two points of
non-differentiability, and that the permutation matrix at a given time
converges to a certain deterministic measure with absolutely continuous and
singular parts. The absorbing state (where all particles are in decreasing
order) is reached at time $(2+o(1))n$. The finishing times of individual
particles converge to deterministic limits, with fluctuations asymptotically
governed by the Tracy--Widom distribution.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph