Related papers: Asymptotic behavior and distributional limits of p…

This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…

Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…

We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erd\H{o}s-R\'{e}nyi random graph $G(n,p)$. This limit can be described as a nonlinear transformation…

A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of…

We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…

Consider a `dense' Erd\H{o}s--R\'enyi random graph model $G=G_{n,M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M/\binom{n}{2}$ is bounded away from 0 and 1. Fix $k=k(n)$ with $k/n$ bounded away from 0 and~1, and let…

We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned…

Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…

We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…

Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…

We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…