Related papers: Critical Self-Similar Markov Trees
We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the operation of pruning, which cuts…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived…
Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
We explore statistical inference in self-similar conservative fragmentation chains when only approximate observations of the sizes of the fragments below a given threshold are available. This framework, introduced by Bertoin and Martinez…
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…
Using the method of spectral decimation and a modified version of Kirchhoffs Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely…
Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated L\'evy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using L\'evy snake techniques.…
We introduce a new Markov Chain called the Cycle Walk for sampling measures of graph partitions where the partition elements have roughly equal size. Such Markov Chains are of current interest in the generation and evaluation of political…
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…
This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed…
Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
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…
The main purpose of this work is to study self-similar branching Markov chains. First we will construct such a process. Then we will establish certain Limit Theorems using the theory of self-similar Markov processes.
Starting from any graph on $\{1, \ldots, n\}$, consider the Markov chain where at each time-step a uniformly chosen vertex is disconnected from all of its neighbors and reconnected to another uniformly chosen vertex. This Markov chain has a…
We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…