Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality and Fixation in $\Xi$-Wright-Fisher processes with
  frequency-dependent selection   A two-types, discrete-time population model with finite, constant size is
constructed, allowing for a general form of frequency-dependent selection and
skewed offspring distribution. Selection is defined based on the idea that
individuals first choose a (random) number of $\textit{potential}$ parents from
the previous generation and then, from the selected pool, they inherit the type
of the fittest parent. The probability distribution function of the number of
potential parents per individual thus parametrises entirely the selection
mechanism. Using sampling- and moment-duality, weak convergence is then proved
both for the allele frequency process of the selectively weak type and for the
population's ancestral process. The scaling limits are, respectively, a
two-types $\Xi$-Fleming-Viot jump-diffusion process with frequency-dependent
selection, and a branching-coalescing process with general branching and
simultaneous multiple collisions. Duality also leads to a characterisation of
the probability of extinction of the selectively weak allele, in terms of the
ancestral process' ergodic properties.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat