Related papers: The valuative tree

Let $C$ be a curve and $V \to C$ an orthogonal vector bundle of rank $r$. For $r \le 6$, the structure of $V$ can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of…

Given a graph $G$, a labeling of $G$ is an injective function $f:V(G)\rightarrow\mathbb{Z}_{\ge 0}$. Under the labeling $f$, the label of a vertex $v$ is $f(v)$, and the induced label of an edge $uv$ is $|f(u) - f(v)|$. The labeling $f$ is…

We consider the algebraic structure of $\mathbb{N}$-graded vertex operator algebras with conformal grading $V=\oplus_{n\geq 0} V_n$ and $\dim V_0\geq 1$. We prove several results along the lines that the vertex operators $Y(a, z)$ for $a$…

This work builds upon the recent monograph [5] on self-similar Markov trees. A self-similar Markov tree is a random real tree equipped with a function from the tree to $[0,\infty)$ that we call the decoration. Here, we construct local time…

Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…

Let $G = (V,E)$ denote a simple graph with the vertex set $V$ and the edge set $E$. The profile of a vertex set $V'\subseteq V$ denotes the multiset of pairwise distances between the vertices of $V'$. Two disjoint subsets of $V$ are…

We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…

The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…

This paper addresses several structural aspects of the insertion-elimination algebra, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the…

Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…

We associate with a plane meromorphic curve f a tree model T(f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobien J(f,g)) in terms of T(f) (resp. T(fg)). We also characterize the…

We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…

We define decorated $\alpha$-stable trees which are informally obtained from an $\alpha$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $\alpha$-stable looptrees of Curien and Kortchemski, where…

We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone $\mathfrak{C}$ has a barycenter. This barycenter is unique, and the barycenter map $\beta$ is continuous, hence is the structure map…

A vector balleans is a vector space over $\mathbb{R}$ endowed with a coarse structure in such a way that the vector operations are coarse mappings. We prove that, for every ballean $(X, \mathcal{E})$, there exists the unique free vector…

Let $T$ be a tree with a given adjacency eigenvalue $\lambda$. In this paper, by using the $\lambda$-minimal trees, we determine the structure of trees with a given multiplicity of the eigenvalue $\lambda$. Furthermore, we consider the…

Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet $X$ and output alphabet $Y$ can be naturally endowed with the quotient of the Euclidean topology by the…

This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local algebra over an algebraically closed field, when treated as a…

The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on symmetric tree weights which define a measure on the set of…

The reduced ring order (rr-order) is a natural partial order on a reduced ring $R$ given by $r\le_{\text{rr}} s$ if $r^2=rs$. It can be studied algebraically or topologically in rings of the form $\text{C}(X)$. The focus here is on those…