Journal ArticleDOI
On a daley-kendall model of random rumours
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TLDR
In this article, it was shown that the number of eventual knowers is asymptotically normal with mean and variance linear in a population consisting of N individuals, and the conjecture was confirmed.Abstract:
Suppose that a certain population consists of N individuals. One member initially learns a rumour from an outside source, and starts telling it to other members, who continue spreading the information. A knower becomes inactive once he encounters somebody already informed. Daley and Kendall, who initiated the study of this model, conjectured that the number of eventual knowers is asymptotically normal with mean and variance linear in N. Our purpose is to confirm this conjecture.read more
Citations
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Theory of rumour spreading in complex social networks
TL;DR: This work introduces a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet).
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Sudden Emergence of a Giantk-Core in a Random Graph
TL;DR: These proofs are based on the probabilistic analysis of an edge deletion algorithm that always find ak-core if the graph has one, and demonstrate that, unlike the 2-core, when ak- core appears for the first time it is very likely to be giant, of size ?pk(?k)n.
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SIHR rumor spreading model in social networks
TL;DR: The model extends the classical Susceptible-Infected-Removed (SIR) rumor spreading model by adding a direct link from ignorants to stiflers and a new kind of people-Hibernators and derive mean-field equations that describe the dynamics of the SIHR model in social networks.
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Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks
TL;DR: The SIHR rumor spreading model with consideration of the forgetting and remembering mechanisms was studied in homogeneous networks is refined and mean-field equations are derived to describe the dynamics of the rumors spreading model in inhomogeneous networks.
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On tree census and the giant component in sparse random graphs
TL;DR: The random sequence {[tn(k) ‐ nh(k)]n−1/2} is shown to be Gaussian in the limit n →∞, and it is proven that almost surely the giant component consists of a giant two‐connected core of size about n(1 − T)β and a “mantle” of trees, and possibly few small unicyclic graphs, each sprouting from its own vertex of the core.
References
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Book
A first course in stochastic processes
Samuel Karlin,Howard M. Taylor +1 more
TL;DR: In this paper, the Basic Limit Theorem of Markov Chains and its applications are discussed and examples of continuous time Markov chains are presented. But they do not cover the application of continuous-time Markov chain in matrix analysis.
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The proportion of the population never hearing a rumour
TL;DR: For a model of a rumour, first given a non-rigorous treatment by Maki and Thompson, it was shown that the proportion of the population never hearing the rumour converges in probability to 0.203 as the population size tends to oo.
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Threshold limit theorems for some epidemic processes
Bengt Von Bahr,Anders Martin-Löf +1 more
TL;DR: In this paper, the Reed-Frost model for the spread of an infection is considered and limit theorems for the total size, T, of the epidemic are proved in the limit when n, the initial number of healthy persons, is large and the probability of an encounter between a healthy and an infected person per time unit, p, is λ/n.
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On a functional central limit theorem for markov population processes
TL;DR: In this paper, the authors investigated the convergence of continuous time Markov population processes on an n-dimensional integer lattice to a Gaussian diffusion, where $(t) is the deterministic approximation to N-IXN (t), and a method of deriving higher order asymptotic expansions for its distribution was justified.