Related papers: Local limit theorem for joint subgraph counts

We generalise the Erdos-Renyi limit theorem on the maximum of the partial sums of random variables to the case when the number of terms in these sums is randomly distributed. Certain relations between the limiting theorems of this type and…

We establish a multivariate local limit theorem for the order and size as well as several other parameters of the k-core of the Erdos-Renyi graph. The proof is based on a novel approach to the k-core problem that replaces the meticulous…

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…

We generalize ultraproducts and local-global limits of graphs to hypergraphs and other structures. We show that the local statistics of an ultraproduct of a sequence of hypergraphs are the ultralimits of the local statistics of the…

We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

We prove part of a conjecture by Johansson, Kahn and Vu \cite{JKV} regarding threshold functions for the existence of an $H$-factor in a random graph \gnp. We prove that the conjectured threshold function is correct for any graph $H$ which…

We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…

The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erd\H{o}s-R\'enyi random graph $G(n,m)$. Our approach is based on applying Freedman's inequalities…

The local chromatic number of a graph was introduced by Erdos et al. in 1986. It is in between the chromatic and fractional chromatic numbers. This motivates the study of the local chromatic number of graphs for which these quantities are…

We show that for each $r\ge 4$, in a density range extending up to, and slightly beyond, the threshold for a $K_r$-factor, the copies of $K_r$ in the random graph $G(n,p)$ are randomly distributed, in the (one-sided) sense that the…

In this paper we consider two-opinion voter models on dynamic random graphs, in which the joint dynamics of opinions and graphs acts as one-way feedback, i.e., edges appear and disappear over time depending on the opinions of the two…

In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…

We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function $W(x,y)$ on the unit square, with $x$ and $y$ uniform on the interval $(0,1)$.…

In this paper we consider the Erd\H{o}s-R\'enyi random graph in the sparse regime in the limit as the number of vertices $n$ tends to infinity. We are interested in what this graph looks like when it contains many triangles, in two…

We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.

Let $G=(V,E)$ be a finite graph. For $v\in V$ we denote by $G_v$ the subgraph of $G$ that is induced by $v$'s neighbor set. We say that $G$ is $(a,b)$-regular for $a>b>0$ integers, if $G$ is $a$-regular and $G_v$ is $b$-regular for every…

A graph $G$ is said to be $p$-locally dense if every induced subgraph of $G$ with linearly many vertices has edge density at least $p$. A famous conjecture of Kohayakawa, Nagle, R\"odl, and Schacht predicts that locally dense graphs have,…

We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural ``limit object'', namely a symmetric measurable 2-variable…

Starting with the large deviation principle (LDP) for the Erd\H{o}s-R\'enyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph…