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In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…
Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the…
Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some…
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of a previous work, where the homogeneous Erd\H os-R\'enyi…
We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…
We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha > d$, we provide a set of sufficient conditions under which the upper…
Exponential random graph models (ERGMs) are widely used for modeling social networks observed at one point in time. However the computational difficulty of ERGM parameter estimation has limited the practical application of this class of…
In this paper, we study the edge eigenvalues of random geometric graphs (RGGs) generated by multivariate Gaussian samples in the sparse regime under a broad class of distance metrics. Previous work on edge eigenvalues under related setups…
For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number…
When the rate parameter of the exponential distribution is associated with predictors, then the main interest will be how to estimate the regression parameter. In this paper, we will investigate how to estimate the parameter on the…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
We study the spectrum of a random multigraph with a degree sequence ${\bf D}_n=(D_i)_{i=1}^n$ and average degree $1 \ll \omega_n \ll n$, generated by the configuration model, and also the spectrum of the analogous random simple graph. We…
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 show that the number $g_n$ of labelled series-parallel graphs on $n$ vertices is asymptotically $g_n \sim g\cdot n^{-5/2} \gamma^n n!$, where $\gamma$ and $g$ are explicit computable constants. We show that the number of edges in random…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…
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…