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Methods and Proofs for the Fisher–Wright Model with Two Types

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2092)

Abstract

The proofs of the results formulated in Section 2 require precise information on the laws of a tagged site (colony) and the total mass. These laws are determined by the collection of joint moments which we can calculate using the dual process \((\eta _{t},\mathcal{F}_{t}^{+})_{t\geq 0}\). To carry out the analysis of the limiting behaviour as N we must develop the asymptotic analysis of the dual process and this is the main objective of this section. Section 8 therefore introduces the principal tools, namely the analysis of the dual particle system in the so-called pre-collision and post-collision regimes (referring to asymptotically self-avoiding or non-self-avoiding migration of the complete dual population) using ideas from the theory of Crump–Mode–Jagers branching processes and the dynamical law of large numbers, that form together the basis for the proofs of the main results.

Keywords

  • Particle Duality
  • Dual Population
  • Dual Process
  • McKean Vlasov
  • Purple Particles

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Dawson, D.A., Greven, A. (2014). Methods and Proofs for the Fisher–Wright Model with Two Types. In: Spatial Fleming-Viot Models with Selection and Mutation. Lecture Notes in Mathematics, vol 2092. Springer, Cham. https://doi.org/10.1007/978-3-319-02153-9_8

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