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Linear functionals of eigenvalues of random matrices
Let Mn be a random n×n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces…
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Probability and Real Trees
Around the Continuum Random Tree.- R-Trees and 0-Hyperbolic Spaces.- Hausdorff and Gromov-Hausdorff Distance.- Root Growth with Re-Grafting.- The Wild Chain and other Bipartite Chains.- Diffusions on…
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Construction of markovian coalescents
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Estimating Allele Age and Selection Coefficient from Time-Serial Data
TLDR
A likelihood method to jointly estimate the selection coefficient and the age of an allele from time-serial data is developed and is illustrated with an application to several loci encoding coat color in horses, a pattern that has previously been linked with domestication.
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Non-equilibrium theory of the allele frequency spectrum.
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Rayleigh processes, real trees, and root growth with re-grafting
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree.…
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The phylogenetic Kantorovich–Rubinstein metric for environmental sequence samples
TLDR
It is established that, if the authors equate a metagenomic sample with its empirical distribution on a reference phylogenetic tree, then the weighted UniFrac distance between two samples is just the classical Kantorovich-Rubinstein, or earth mover's, distance between the corresponding empirical distributions.
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Invariants of Some Probability Models Used in Phylogenetic Inference
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Edge Principal Components and Squash Clustering: Using the Special Structure of Phylogenetic Placement Data for Sample Comparison
TLDR
Two new complementary methods that leverage how this microbial community data sits on a phylogenetic tree and illustrate their use with data from the human microbiome are presented.
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Measure-Valued Branching Diffusions with Singular Interactions
Abstract The usual super-Brownian motion is a measure-valued process that arises as a high density limit of a system of branching Brownian particles in which the branching mechanism is critical. In…
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