Related papers: Numerical Approach to Central Limit Theorem for Bi…
In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…
Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this…
We consider so-called simple families of labelled trees, which contain, e.g., ordered, unordered, binary and cyclic labelled trees as special instances, and study the global and local behaviour of the number of inversions. In particular we…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they…
We study the average height of random trees generated by leaf-centric binary tree sources as introduced by Zhang, Yang and Kieffer. A leaf-centric binary tree source induces for every $n \geq 2$ a probability distribution on the set of…
A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
We study the average number of distinct fringe subtrees in random trees generated by leaf-centric binary tree sources as introduced by Zhang, Yang and Kieffer. A leaf-centric binary tree source induces for every $n \geq 2$ a probability…
In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…
The critical beta-splitting tree, introduced by Aldous, is a Markov branching phylogenetic tree. Aldous and Pittel recently proved, amongst other results, a central limit theorem for the height of a random leaf. We give an alternative…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…
Processing sentence constituency trees in binarised form is a common and popular approach in literature. However, constituency trees are non-binary by nature. The binarisation procedure changes deeply the structure, furthering constituents…
We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…