Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplified Forms of the Transition Probabilities of the Two-Species ASEP
  with Some Initial Orders of Particles   It has been known that the transition probability of the single species ASEP
with $N$ particles is expressed as a sum of $N!$ $N$-fold contour integrals
which are related to permutations in the symmetric group $S_N$. On other hand,
the transition probabilities of the multi-species ASEP, in general, may be
expressed as a sum of much more terms than $N!$. In this paper, we show that if
the initial order of species is given by $2\cdots 21$, $12\cdots 2$, $1\cdots
12$ or $21\cdots 1$, then the transition probabilities can be expressed as a
sum of at most $N!$ contour integrals, and provide their formulas explicitly.

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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph