Related papers: A Markovian growth dynamics on rooted binary trees…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…
We introduce a non-increasing tree growth process $((T_n,\sigma_n),\, n\ge 1)$, where $T_n$ is a rooted labeled tree on $n$ vertices and ${\sigma}_n$ is a permutation of the vertex labels. The construction of $(T_{n},{\sigma}_n)$ from…
We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection…
The mother-dependent neutral mutations model describes the evolution of a population across discrete generations, where neutral mutations occur among a finite set of possible alleles. In this model, each mutant child acquires a type…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…
We consider stochastic processes with (or without) memory whose evolution is encoded by a finite or infinite rooted tree. The main goal is to compare the entropy rates of a given base process and a second one, to be considered as a…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
We present an evolutionary self-governing model based on the numerical atomic rule $Z(a,b)=ab/\gcd(a,b)^2$, for $a,b$ positive integers. Starting with a sequence of numbers, the initial generation $Gin$, a new sequence is obtained by…
We are interested in the asymptotics of random trees built by linear preferential attachment, also known in the literature as Barab\'asi-Albert trees or plane-oriented recursive trees. We first prove a conjecture of Bubeck, Mossel \& R\'acz…
We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…
We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We…
We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…
We consider the tributary structure of Howard's drainage model studied by Gangopadhyay et. al. Conditional on the event that the tributary survives up to time $n$, we show that, as a sequence of random metric spaces, scaled tributary…
The Marked Binary Branching Tree (MBBT) is the family tree of a rate one binary branching process, on which points have been generated according to a rate one Poisson point process, with i.i.d. uniformly distributed activation times…
We consider a sequence of Markov chains $(\mathcal X^n)_{n=1,2,...}$ with $\mathcal X^n = (X^n_\sigma)_{\sigma\in\mathcal T}$, indexed by the full binary tree $\mathcal T = \mathcal T_0 \cup \mathcal T_1 \cup ...$, where $\mathcal T_k$ is…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…