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Genealogical Properties of Subsamples in Highly Fecund Populations
We consider some genealogical properties of nested samples. The complete sample is assumed to have been drawn from a natural population characterised...
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Lines of Descent Under Selection
We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We...
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Small-Particle Limits in a Regularized Laplacian Random Growth Model
We study a regularized version of Hastings–Levitov planar random growth that models clusters formed by the aggregation of diffusing particles. In...
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Permanental Partition Models and Markovian Gibbs Structures
We study both time-invariant and time-varying Gibbs distributions for configurations of particles into disjoint clusters. Specifically, we introduce...
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On Time Dynamics of Coagulation-Fragmentation Processes
We establish a characterization of coagulation-fragmentation processes, such that the induced birth and death processes depicting the total number of...
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Gibbs Distributions for Random Partitions Generated by a Fragmentation Process
In this paper we study random partitions of {1,…, n } where every cluster of size j can be in any of w j possible internal states. The Gibbs ( n , k , w )...