A large deviations principle for the Maki–Thompson rumour model

Lebensztayn, Élcio

doi:10.1016/j.jmaa.2015.06.054

Cited by 11 publications

(10 citation statements)

References 19 publications

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“…In these models we usually have three kinds of individuals: ignorants (those that are yet to discover the rumor), spreaders (those that know the rumor and are spreading it) and stiflers (those that know the rumor, but do not spread it). These models and their variations are already well studied, see for example [4,3,5,6,9]. Differently from the Daley and Kendall or Maki and Thompson models, here we study the propagation of the rumor in discrete time and with no stiflers, so each individual will always propagate the information over time if possible.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Total Flooding Time and Rumor Propagation on Graphs

Camargo

Popov

2017

J Stat Phys

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We study a model of rumor propagation in discrete time where each site in the graph has initially a distinct information; we are interested in the number of "conversations" before the entire graph knows all informations. This problem can be described as a flooding time problem with multiple liquids. For the complete graph we compare the ratio between the expected propagation time for all informations and the corresponding time for a single information, obtaining the asymptotic ratio 3/2 between them.

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Section: Introduction and Resultsmentioning

confidence: 99%

Total Flooding Time and Rumor Propagation on Graphs

Camargo

Popov

2017

J Stat Phys

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“…The previous numerical analysis indicates that, for the Maki-Thompson model in which all spreaders act simultaneously, the limiting fraction of ignorants in the population would be equal to 0.174545. For more on the definitions and limit theorems for stochastic rumour models, we refer to Daley and Gani [11, Chapter 5], Lebensztayn [28], and Lebensztayn et al [32].…”

Section: Limiting Proportion Of Unvisited Verticesmentioning

confidence: 99%

Laws of large numbers for the frog model on the complete graph

Lebensztayn

Estrada

2019

Journal of Mathematical Physics

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The frog model is a stochastic model for the spreading of an epidemic on a graph, in which a dormant particle starts to perform a simple random walk on the graph and to awake other particles, once it becomes active. We study two versions of the frog model on the complete graph with N + 1 vertices. In the first version we consider, active particles have geometrically distributed lifetimes. In the second version, the displacement of each awakened particle lasts until it hits a vertex already visited by the process. For each model, we prove that as N → ∞, the trajectory of the process is well approximated by a three-dimensional discrete-time dynamical system. We also study the long-term behavior of the corresponding deterministic systems.2010 Mathematics Subject Classification. 60K35, 60J10, 92B05.

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“…In a finite population the process will eventually reach a stack situation where individuals are either stiflers or ignorants. The MT model has been widely studied and, among the rigorous results available, we recall that Sudbury proved that, as the population size tends to infinity, the proportion of the population never hearing the rumour converges in probability to 0.2032 [14]; Watson later derived the asymptotic normality of a suitably scaled version of this proportion [15] and a corresponding large deviations principle, with an explicit formula for the rate function was found by Lebensztayn [16]; we also refer to [18,19,17,20,21,22,23,24] for further investigations on the model. As we said, in the original version of the MT model there was no concern about the structure of the embedding community, but in more recent works, extensions to include also the underlying topology have been addressed [8].…”

Section: Introductionmentioning

confidence: 99%

Phase Transition for the Maki–Thompson Rumour Model on a Small-World Network

et al. 2017

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We consider the Maki-Thompson model for the stochastic propagation of a rumour within a population. We extend the original hypothesis of homogenously mixed population by allowing for a small-world network embedding the model. This structure is realized starting from a k-regular ring and by inserting, in the average, c additional links in such a way that k and c are tuneable parameter for the population architecture. We prove that this system exhibits a transition between regimes of localization (where the final number of stiflers is at most logarithmic in the population size) and propagation (where the final number of stiflers grows algebraically with the population size) at a finite value of the network parameter c. A quantitative estimate for the critical value of c is obtained via extensive numerical simulations.

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A large deviations principle for the Maki–Thompson rumour model

Cited by 11 publications

References 19 publications

Total Flooding Time and Rumor Propagation on Graphs

Total Flooding Time and Rumor Propagation on Graphs

Laws of large numbers for the frog model on the complete graph

Phase Transition for the Maki–Thompson Rumour Model on a Small-World Network

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