Related papers: Random Graphs Associated to some Discrete and Cont…
The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
In a one-parameter model for evolution of random trees, which also includes the Barabasi-Albert random tree, almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. Results about Polya…
We have simulated the two-dimensional $RP^2$ and $RP^3$ $\sigma$-models, at correlation lengths up to about 220 (resp.\ 30), using a Wolff-type embedding algorithm. We see no evidence of asymptotic scaling. Indeed, the data rule out the…
Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models…
Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Association models for a pair of random elements $X$ and $Y$ (e.g., vectors) are considered which specify the odds ratio function up to an unknown parameter $\bolds\theta$. These models are shown to be semiparametric in the sense that they…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…
In this paper, we investigate the diameter in preferential attachment (PA-) models, thus quantifying the statement that these models are small worlds. The models studied here are such that edges are attached to older vertices proportional…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
In this paper we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space due to Atiyah, Bott, and Goldman. Let $\Sigma_{g}$ denote a…
We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the design $A$ is rotationally-invariant in law. In the large system limit as dimension and…