Related papers: Numerical Approach to Central Limit Theorem for Bi…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
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…
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…
We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…
Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…
The Horton-Strahler number of a tree is a measure of its branching complexity; it is also known in the literature as the register function. We show that for critical Galton-Watson trees with finite variance conditioned to be of size $n$,…
The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length $n$ of the martingale. A consequence of the results are Gaussian couplings and a multiplier bootstrap for…
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…
We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution of the…
This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these…
This article presents two novel algorithms for generating random increasing trees. The first algorithm efficiently generates strictly increasing binary trees using an ad hoc method. The second algorithm improves the recursive method for…
We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than {\epsilon} ({\epsilon} > 0). It is known ([BM05]) that the empirical measure of these fragments converges in law, under some…
We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…