Related papers: Limiting distributions of triangle counts in linea…
We investigate the joint distribution of nodes of small degrees and the degree profile in preferential dynamic attachment circuits. In particular, we study the joint asymptotic distribution of the number of the nodes of outdegree $0$…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
Network diffusion models are applicable to many socioeconomic interactions, yet network interaction is hard to observe or measure. Whenever the diffusion process is unobserved, the number of possible realizations of the latent matrix that…
This paper considers the limiting distribution of $\pi_{\lambda,\theta}$, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance \cite{MR1626158}. In \cite{MR2519357} the large deviation principle…
A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…
This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
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…
In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…
We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…
We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
We analyze the 3-parameter family of random networks which are uniform on networks with fixed number of edges, triangles, and nodes (between 33 and 66). We find precursors of phase transitions which are known to be present in the asymptotic…
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…
The spatial preferential attachment (SPA) is a model for complex networks. In the SPA model, nodes are embedded in a metric space, and each node has a sphere of influence whose size increases if the node gains an in-link, and otherwise…