Related papers: From Hammersley's lines to Hammersley's trees
In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…
We study the bounded regions in a generic slice of the hyperplane arrangement in $\mathbb{R}^n$ consisting of the hyperplanes defined by $x_i$ and $x_i+x_j$. The bounded regions are in bijection with several classes of combinatorial…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…
We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…
We study the distribution of the number of leaves of the subtree chosen uniformly at random among all the subtrees of the critical branching process tree at extinction.
We analyse a simple discrete-time stochastic process for the theoretical modeling of the evolution of protein lengths. At every step of the process a new protein is produced as a modification of one of the proteins already existing and its…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total…
Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution…
Subset sampling (also known as Poisson sampling), where the decision to include any specific element in the sample is made independently of all others, is a fundamental primitive in data analytics, enabling efficient approximation by…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
To further develop the statistical inference problem for heterogeneous treatment effects, this paper builds on Breiman's (2001) random forest tree (RFT)and Wager et al.'s (2018) causal tree to parameterize the nonparametric problem using…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…