The maximum proportion of spreaders in stochastic rumor models
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916837320556544 |
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| author | Lebensztayn, Elcio Rodriguez, Pablo M. |
| author_facet | Lebensztayn, Elcio Rodriguez, Pablo M. |
| contents | We examine a general stochastic rumor model characterized by specific parameters that govern the interaction rates among individuals. Our model includes the \((α, p)\)-probability variants of the well-known Daley--Kendall and Maki--Thompson models. In these variants, a spreader involved in an interaction attempts to transmit the rumor with probability \(p\); if successful, any spreader encountering an individual already informed of the rumor has probability \(α\) of becoming a stifler. We prove that the maximum proportion of spreaders throughout the process converges almost surely, as the population size approaches~\(\infty\). For both the classical Daley--Kendall and Maki--Thompson models, the asymptotic proportion of the rumor peak is \(1 - \log 2 \approx 0.3069\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximum proportion of spreaders in stochastic rumor models Lebensztayn, Elcio Rodriguez, Pablo M. Physics and Society Probability 60F15, 60J28, 60G17 We examine a general stochastic rumor model characterized by specific parameters that govern the interaction rates among individuals. Our model includes the \((α, p)\)-probability variants of the well-known Daley--Kendall and Maki--Thompson models. In these variants, a spreader involved in an interaction attempts to transmit the rumor with probability \(p\); if successful, any spreader encountering an individual already informed of the rumor has probability \(α\) of becoming a stifler. We prove that the maximum proportion of spreaders throughout the process converges almost surely, as the population size approaches~\(\infty\). For both the classical Daley--Kendall and Maki--Thompson models, the asymptotic proportion of the rumor peak is \(1 - \log 2 \approx 0.3069\). |
| title | The maximum proportion of spreaders in stochastic rumor models |
| topic | Physics and Society Probability 60F15, 60J28, 60G17 |
| url | https://arxiv.org/abs/2507.07914 |