Related papers: On ballistic deposition process on a strip
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Stick-breaking (SB) processes are often adopted in Bayesian mixture models for generating mixing weights. When covariates influence the sizes of clusters, SB mixtures are particularly convenient as they can leverage their connection to…
We obtain new non-asymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym\'e trees (the family trees of branching processes), in the process settling three…
We study random typical minimal factorizations of the $n$-cycle into transpositions, which are factorizations of $(1, \ldots,n)$ as a product of $n-1$ transpositions. By viewing transpositions as chords of the unit disk and by reading them…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…
The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
In this paper we present a multilayer particle deposition model on a random tree. We derive the time dependent densities of the first and second layer analytically and show that in all trees the limiting density of the first layer exceeds…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
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…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course…