Related papers: Mutations on a Random Binary Tree with Measured Bo…
We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by…
In this work, we give a description of all sigma-finite measures on the space of rooted compact real trees which satisfy a certain regenerative property. We show that any infinite measure which satisfies the regenerative property is the…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals -- each with many genes -- splitting into new populations or species. The coalescent…
We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with $n$ vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of…
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
The vertices of the Cayley graph of a finitely generated semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix, respecting nearest neighbor…
We call a random point measure infinitely ramified if for every $n\in \mathbb N$, it has the same distribution as the $n$-th generation of some branching random walk. On the other hand, branching L\'evy processes model the evolution of a…
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
In [Ald00], Aldous investigates a symmetric Markov chain on cladograms and gives bounds on its mixing and relaxation times. The latter bound was sharpened in [Sch02]. In the present paper we encode cladograms as binary, algebraic measure…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…
The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the "individuals" in…
The basin of infinity of a polynomial map $f : {\bf C} \arrow {\bf C}$ carries a natural foliation and a flat metric with singularities, making it into a metrized Riemann surface $X(f)$. As $f$ diverges in the moduli space of polynomials,…
We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in…
We demonstrate the possibility of coding parts, features that are higher level than boundaries, using a modified AT field after augmenting the interaction term of the AT energy with a non-local term and weakening the separation into…
The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -- also called "histories" -- with a finite number $n$ of leaves. We study the…