Related papers: A note on the limit law of one-sided tree destruct…
In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we…
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…
A tree functional is called additive if it satisfies a recursion of the form $F(T) = \sum_{j=1}^k F(B_j) + f(T)$, where $B_1,\ldots,B_k$ are the branches of the tree $T$ and $f(T)$ is a toll function. We prove a general central limit…
We consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of…
Decision forest algorithms typically model data by learning a binary tree structure recursively where every node splits the feature space into two sub-regions, sending examples into the left or right branch as a result. In axis-aligned…
Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…
We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou [9].…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split…
We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
The first main result of this paper is that the law of the (rescaled) two-dimensional uniform spanning tree is tight in a space whose elements are measured, rooted real trees continuously embedded into Euclidean space. Various properties of…
We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient…
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…
We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…
We prove the existence of a limit of the finite volume probability measures generated by tree growth rules in Ford's alpha model of phylogenetic trees. The limiting measure is shown to be concentrated on the set of trees consisting of…
We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity…
In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer…
We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P\'olya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity.…
This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees.…