Related papers: Numerical Approach to Central Limit Theorem for Bi…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…
Let $\Omega_n$ be the family of binary trees on $n$ vertices obtained by identifying the root of an rgood binary tree with a vertex of maximum eccentricity of a binary caterpillar. In the paper titled "On different middle parts of a tree…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…
The hierarchical Dirichlet process is a discrete random measure used as a prior in Bayesian nonparametrics and motivated by the study of groups of clustered data. We study the asymptotic behavior of the power sum symmetric polynomials for…
We consider a supercritical general branching population where the lifetimes of individuals are i.i.d. with arbitrary distribution and each individual gives birth to new individuals at Poisson times independently from each others. The…
For fixed $t\ge 2$, we consider the class of representations of $1$ as sum of unit fractions whose denominators are powers of $t$ or equivalently the class of canonical compact $t$-ary Huffman codes or equivalently rooted $t$-ary plane…
The Horton-Strahler number of a rooted tree $T$ is the height of the tallest complete binary tree that can be homeomorphically embedded in $T$. The number of full binary trees with $n$ internal vertices and Horton-Strahler number $s$ is…
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
In Chapter 1 we fully characterise pairs of finite graphs which form a gap in the full homomorphism order. This leads to a simple proof of the existence of generalised duality pairs. We also discuss how such results can be carried to…
Loss tomography has received considerable attention in recent years and a number of estimators based on maximum likelihood (ML) or Bayesian principles have been proposed. Almost all of the estimators are devoted to the tree topology despite…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure…
Four types of explicit estimators are proposed here to estimate the loss rates of the links in a network with the tree topology and all of them are derived by the maximum likelihood principle. One of the four is developed from an estimator…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…