Related papers: Stochastic homogenization of horospheric tree prod…
Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian…
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of…
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of…
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological tree'. In this work, we are interested in the continuum…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree…
If $M$ is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on $\tm$ a quasi-invariant transverse measure for the horospherical foliation, and prove that this measure is uniquely determined by its…
In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…