相关论文: Ultrametric and tree potential

Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like…

A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…

We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…

The Martin compactification is investigated for a d-dimensional random walk which is killed when at least one of it's coordinates becomes zero or negative. The limits of the Martin kernel are represented in terms of the harmonic functions…

We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using…

Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices…

We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…

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…

We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated…

We consider a countable tree $T$, possibly having vertices with infinite degree, and an arbitrary stochastic nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with…

Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel tower a canonical electrical network on the word tree whose edge weights are the diagonal increments. This converts diagonal…

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 Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We…

We study extremal properties of finite ultrametric spaces $X$ and related properties of representing trees $T_X$. The notion of weak similarity for such spaces is introduced and related morphisms of labeled rooted trees are found. It is…

We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated…

The transition matrix of a Markov chain $(X_k,k\geq 0)$ on a finite or infinite rooted tree is said to be almost upper-directed if, given $X_k$, the node $X_{k+1}$ is either a descendant of $X_k$ or the parent of $X_k$. It is said to be…

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…

Ultrametric matrices are a class of covariance matrices that arise in latent tree models. As a parameter space in a statistical model, the set of ultrametric matrices is neither convex nor a smooth manifold. Focus in the literature has…

Let T be an infinite homogenous tree of homogeneity $q+1$. Attaching to each edge the conductance $1$, the tree will became an electric network. The reversible Markov chain associated to this network is the simple random walk on the…

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…