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Abstract:
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We review some recent constructions of time-dependent random probability measures of Gibbs type which exhibit diffusive behaviour. The characterization of the dynamics of the type frequencies, and those of the type heterogeneity in the underlying population, also known as alpha diversity, allows for a qualitative classification of these models according to whether the heterogeneity is driven by state-dependent quantities and whether the frequencies dynamics are directly affected by the overall heterogeneity.
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