Related papers: Asymptotic quantization of exponential random grap…
We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…
We present a set of conditions which, if satisfied, provide for a complete asymptotic analysis of random matrices with source term containing two distinct eigenvalues. These conditions are shown to be equivalent to the existence of a…
A fundamental problem in pattern avoidance is describing the asymptotic behavior of the extremal function and its generalizations. We prove an equivalence between the asymptotics of the graph extremal function for a class of bipartite…
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward $p$-stars. Our models are close cousins of exponential random graph models (ERGMs), in which edges and certain other subgraph…
We prove that the asymptotic entropy of large simple graphs, as a function of fixed edge and triangle densities, is nondifferentiable along a certain curve.
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
We consider the edge-triangle model (or Strauss model), and focus on the asymptotic behavior of the triangle density when the size of the graph increases to infinity. This random graph belongs to the class of exponential random graphs,…
The asymptotic behavior of the Jaccard index in $G(n,p)$, the classical Erd\"{o}s-R\'{e}nyi random graphs model, is studied in this paper, as $n$ goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two…
We establish the asymptotic behaviour of $\mu(G(n,p))$, the number of unlabelled induced subgraphs in the binomial random graph $G(n,p)$, for almost the entire range of the probability parameter $p=p(n)\in[0,1]$. In particular, we show that…
A graph property is said to be elusive ( evasive) if every algorithm testing this property by asking questions of the form "is there an edge between vertices x and y" requires, in the worst case, to ask about all pairs of vertices. The…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…