相关论文: Limit theorems for sequences of random trees
Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random…
We prove limit theorems for sums of functions of subtrees of binary search trees and random recursive trees. In particular, we give simple new proofs of the fact that the number of fringe trees of size $ k=k_n $ in the binary search tree…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…
In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the…
In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to…
Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b \ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the…
A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
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 study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…
Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…
We study tree-indexed random walks as introduced by Benjamini, H\"aggstr\"om, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conjecture of those authors that the distribution of the…
Kesten and Lee [36] proved that the total length of a minimal spanning tree on certain random point configurations in $\mathbb{R}^d$ satisfies a central limit theorem. They also raised the question: how to make these results quantitative?…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.