Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality between box-ball systems of finite box and/or carrier capacity   We construct the dynamics of the box-ball system with box capacity $J$ and
carrier capacity $K$, which we abbreviate to BBS($J$,$K$), in the case of
infinite initial configurations, and show that this system is dual to the
analogous BBS($K$,$J$) model. Towards this end, we build on previous work for
the original box-ball system, that is BBS($1$,$\infty$), to show that when the
box capacity $J$ and carrier capacity $K$ satisfy $J<K$ the dynamics can be
represented by a Pitman-type transformation. These ideas are applied in the
case of random initial configurations to show that the distributional
properties of spatial stationarity and invariance under the BBS dynamics are
dual. Moreover, for independent and identically distributed configurations, we
derive a characterisation of invariant measures in terms of a detailed balance
equation, which captures the duality of the system locally; this is used to
find all invariant measures in this class. Finally, we deduce the speed of a
tagged particle, and show that this also satisfies a natural duality relation.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th