Related papers: Decorated stable trees
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
Recently, a phase transition phenomenon has been established for parking on random trees. We extend the results of Curien and H\'enard on general Galton--Watson trees and allow different car arrival distributions depending on the vertex…
In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…
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…
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t), t>=0)$ out of this tree by removing the vertices located under height $t$. Thanks to a…
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable…
We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha \in (1,2)$.…
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert…
We study notions of hyperuniformity for invariant locally square-integrable point processes in regular trees. We show that such point processes are never geometrically hyperuniform, and if the diffraction measure has support in the…
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
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 a rooted tree of size $n$ is proved to…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…
We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other…
We introduce a general recursive method to construct continuum random trees (CRTs) from independent copies of a random string of beads, that is, any random interval equipped with a random discrete probability measure, and from related…