Related papers: Scaling limits for some random trees constructed i…

Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…

We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton--Watson trees and similar but less well-known results in…

We show that every connected graph can be approximated by a normal tree, up to some arbitrarily small error phrased in terms of neighbourhoods around its ends. The existence of such approximate normal trees has consequences of both…

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…

Panagiotou and Stufler recently proved an important fact on their way to establish the scaling limits of random P\'olya trees: a uniform random P\'olya tree of size $n$ consists of a conditioned critical Galton-Watson tree $C_n$ and many…

Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests, they are self-similar objects that further satisfy a Markov…

We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…

A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…

This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…

Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning and are often viewed as…

Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a…

Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a…

We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…

The continuum random tree is the scaling limit of the uniform spanning tree on the complete graph with $N$ vertices. The Aldous-Broder chain on a graph $G=(V,E)$ is a discrete-time stochastic process with values in the space of rooted trees…