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Majority dynamics on trees and the dynamic cavity method
Voters independent distribution random variables the initialization
2015/8/20
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...
Random Walks on Trees and Matchings
Markov Chain Matchings Phylogenetic Tree Fourier analysis Zonal polynomials Coagulation-Fragmentation
2015/7/8
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...
Single--crossover recombination and ancestral recombination trees
population genetics recombination segmentation process ancestral trees
2012/6/21
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...
Galton-Watson trees with vanishing martingale limit
Conditioning principle large deviations micro-canonical distribution sharp thresholds branching entropic repulsion
2012/4/16
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...
Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on Z^2
Uniform spanning tree loop-erased random walk abelian sandpile model
2011/9/14
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...
The asymptotic distribution of the length of Beta-coalescent trees
Beta-coalescent coupling, point process stable distribution Probability
2011/9/6
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...
Branching Markov processes on fragmentation trees generated from the paintbox process
Branching Markov processes fragmentation trees the paintbox process Probability
2011/9/5
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...
Schroder's problems and scaling limits of random trees
Schroder's problems Probability scaling limits of random trees
2011/8/31
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...
An algebraic analysis of the two state Markov model on tripod trees
Phylogenetics Identi ability Invariant Two-State-Model
2011/3/1
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...
Random Gaussian sums on trees
Gaussian processes processes indexed by trees bounded processes
2011/1/21
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...
The distribution of height and diameter in random non-plane binary trees
distribution of height diameter in random non-plane binary trees
2010/12/1
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...