Related papers: Degree asymptotics with rates for preferential att…
We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet.…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
We study a new kind of proximity graphs called proportional-edge proximity catch digraphs (PCDs)in a randomized setting. PCDs are a special kind of random catch digraphs that have been developed recently and have applications in statistical…
Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution…
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in…
We consider a string with fixed endpoints where the mass density and/or the elastic coefficient vary in a self-affine way as function of position. It is demonstrated how the eigenvalues in the asymptotic limit are distributed. Scaling laws…
Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible target distributions. We do so by using the generator approach…
We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…
We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
There has been a lot of research on random graph models for large real-world networks such as those formed by hyperlinks between web pages in the world wide web. Though largely successful qualitatively in capturing their key properties,…
Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this…
In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a principal submatrix of a Hermitian matrix and…
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
We study the asymptotic growth rate of the label size of high-degree vertices in weighted recursive graphs (WRG) when the weights are i.i.d. almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and…