Abstract
In this paper we study the Maki-Thompson rumor model on infinite Cayley trees. The basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals: ignorants, spreaders and stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other (nearest neighbor) spreaders, or stiflers. In this work we study this model on infinite Cayley trees, which is formulated as a continuous-times Markov chain, and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.
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Acknowledgements
Part of this work has been developed during a visit of V.V.J. to the ICMC-University of São Paulo and a visit of P.M.R. to the IME-Federal University of Goiás. The authors thank these institutions for the hospitality and support. Special thanks are also due to the two anonymous reviewers for their helpful comments and suggestions.
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Communicated by Deepak Dhar.
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This work has been developed with support of the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES), Financial Code 001. This work has been supported also by FAPESP (2017/10555-0), CNPq (Grant 304676/2016-0), and CAPES (under the Program MATH-AMSUD/CAPES 88881.197412/2018-01)
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Junior, V.V., Rodriguez, P.M. & Speroto, A. The Maki-Thompson Rumor Model on Infinite Cayley Trees. J Stat Phys 181, 1204–1217 (2020). https://doi.org/10.1007/s10955-020-02623-y
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DOI: https://doi.org/10.1007/s10955-020-02623-y