Related papers: Mass distribution exponents for growing trees
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of the X_i and…
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…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase…
We first consider the growth of trees by probabilistic attachment of new vertices to leaves. This leads to a growth model based on vertex clusters and probabilities assigned to clusters. This model turns out to be readily applicable to…
This paper extends the study of fringe trees in random plane trees with a given degree statistic. While previous work established the asymptotic normality of the count of fringe trees isomorphic to a fixed tree, we investigate the case…
We consider maximum rooted tree extension counts in random graphs, i.e., we consider M_n = \max_v X_v where X_v counts the number of copies of a given tree in G_{n,p} rooted at vertex v. We determine the asymptotics of M_n when the random…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
In this work, we investigate the spectrum of singularities of random stable trees with parameter $\gamma\in(1,2)$. We consider for that purpose the scaling exponents derived from two natural measures on stable trees: the local time $\ell^a$…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
Cascade models are central to understanding, predicting, and controlling epidemic spreading and information propagation. Related optimization, including influence maximization, model parameter inference, or the development of vaccination…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a…
We investigate vertex levels of containment in a random hypergraph grown in the spirit of a recursive tree. We consider a local profile tracking the evolution of the containment of a particular vertex over time, and a global profile…
We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…
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…
To each sequence $(a_n)$ of positive real numbers we associate a growing sequence $(T_n)$ of continuous trees built recursively by gluing at step $n$ a segment of length $a_n$ on a uniform point of the pre-existing tree, starting from a…