Related papers: Tree approximation in quasi-trees

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by DAG compression. A method for quantifying the degree of self-similarity of plants through self-nested trees has been…

We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…

Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalize these strategies by viewing any geodesic metric space as a…

We generalize Schwenk's result that almost all trees contain any given limb to trees with positive integer vertex weights. The concept of characteristic polynomial is extended to such weighted trees and we prove that the proportion of…

We construct quasi-isometry invariants of a one-ended finitely presented group by considering the tree of cylinders of a two-ended JSJ decomposition of the group. When the group satisfies additional quasi-isometric rigidity hypotheses we…

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…

Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…

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 introduce and geometrically characterize the notion of uniformly perfect Morse boundary for proper geodesic metric spaces. As a unifying result, we prove that the Morse boundary of any finitely generated, non-elementary group is…

Let X be a geodesic metric space. Gromov proved that there exists k>0 such that if every sufficiently large triangle T satisfies the Rips condition with constant k times pr(T), where pr(T) is the perimeter T, then X is hyperbolic. We give…

We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…

We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…

We classify the groups quasi-isometric to a group generated by finite-order elements within the class of one-ended hyperbolic groups which are not Fuchsian and whose JSJ decomposition over two-ended subgroups does not contain rigid vertex…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

We use the language of proper CAT(-1) spaces to study thick, locally compact trees, the real, complex and quaternionic hyperbolic spaces and the hyperbolic plane over the octonions. These are rank 1 Euclidean buildings, respectively rank 1…

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Doucha, Nies, and Tsankov, which are largely incompatible. With this we explicitly exhibit…

In \cite{LuLa13}, two of the authors initiated a study of Lipschitz equivalence of self-similar sets through the augmented trees, a class of hyperbolic graphs introduced by Kaimanovich \cite{Ka03} and developed by Lau and Wang…

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 the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…