Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A modified lookdown construction for the Xi-Fleming-Viot process with
  mutation and populations with recurrent bottlenecks   Let $\Lambda$ be a finite measure on the unit interval. A
$\Lambda$-Fleming-Viot process is a probability measure valued Markov process
which is dual to a coalescent with multiple collisions ($\Lambda$-coalescent)
in analogy to the duality known for the classical Fleming Viot process and
Kingman's coalescent, where $\Lambda$ is the Dirac measure in 0.
  We explicitly construct a dual process of the coalescent with simultaneous
multiple collisions ($\Xi$-coalescent) with mutation, the $\Xi$-Fleming-Viot
process with mutation, and provide a representation based on the empirical
measure of an exchangeable particle system along the lines of Donnelly and
Kurtz (1999). We establish pathwise convergence of the approximating systems to
the limiting $\Xi$-Fleming-Viot process with mutation. An alternative
construction of the semigroup based on the Hille-Yosida theorem is provided and
various types of duality of the processes are discussed.
  In the last part of the paper a population is considered which undergoes
recurrent bottlenecks. In this scenario, non-trivial $\Xi$-Fleming-Viot
processes naturally arise as limiting models.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: physics