Related papers: Recursive functions on conditional Galton--Watson …
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, $Z$ say, is in the domain of attraction of a stable law with index…
We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random…
We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called Levy trees. This extends previous results due to several authors.
We give a realization of the stable L\'evy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent…
A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of transversals of size k in a rooted tree T. We define a partial order on the set of all rooted trees with n…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
We consider the graph dynamical systems known as k-reversible processes. In such processes, each vertex in the graph has one of two possible states at each discrete time step. Each vertex changes its state between the current time and the…
In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…
We prove limit theorems for sums of functions of subtrees of binary search trees and random recursive trees. In particular, we give simple new proofs of the fact that the number of fringe trees of size $ k=k_n $ in the binary search tree…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
We consider Galton-Watson trees associated with a critical offspring distribution and conditioned to have exactly $n$ vertices. These trees are embedded in the real line by affecting spatial positions to the vertices, in such a way that the…
We consider a branching random walk (BRW) taking its values in the $\mathtt{b}$-ary rooted tree $\mathbb W_{ \mathtt{b}}$ (i.e. the set of finite words written in the alphabet $\{ 1, \ldots, \mathtt{b} \}$, with $\mathtt{b}\! \geq \! 2$).…
We consider the Ising model on a supercritical Galton-Watson tree $\mathbf{T}_n$ of depth $n$ with a sparse random external field, given by a collection of i.i.d. Bernouilli random variables with vanishing parameter $p_n$. This may me…
We consider a super-critical Galton-Watson tree whose non-degenerate offspring distribution has finite mean. We consider the random trees $\tau$n distributed as $\tau$ conditioned on the n-th generation, Zn, to be of size an $\in$ N. We…
We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of…