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On rigidity of infinite exchangeable sequences
Maximillian Newman
We ask when the law of an infinite exchangeable sequence is uniquely determined by a finite-dimensional marginal. For mixtures of a probability kernel, a weak localization conditio…
Rigidity of infinite exchangeable sequences with Gaussian marginals
Maximillian Newman
We study infinite exchangeable sequences with Gaussian one-dimensional marginals. We formulate the conjecture that joint Gaussianity of a single pair of coordinates forces the enti…
The quenched coalescent for structured diploid populations with large migrations and uneven offspring distributions
Maximillian Newman
In this work we describe a new model for the evolution of a diploid structured population backwards in time that allows for large migrations and uneven offspring distributions. The…
Quenched coalescent for diploid population models with selfing and overlapping generations
Louis Wai-Tong Fan, Maximillian Newman, John Wakeley
We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of genes as the population siz…