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An elector sits on each vertex of an in nite tree of degree k, and has to decide between two alternatives.At each time step, each elector switches to the opinion of the majority of her neighbors. We a...
We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vert...
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the...
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, agrees up to generation $K$ with a regular $\mu$-ary tree, where $\mu$ is the essential mini...
Abstract: We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "i...
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
Abstract: A fragmentation of a set $A$ is a graph with vertices labeled by subsets of $A$ which obey a certain parent-child relationship. A random fragmentation tree is a probability distribution on t...
Abstract: In a classic paper Schr\"oder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on averag...
Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood.Here, we investigate the two...
Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (Xt)t∈T represented as Xt = σ(t) X vt α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i...
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of...

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