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Doctoral Thesis
DOI
https://doi.org/10.11606/T.104.2021.tde-23062021-142435
Document
Author
Full name
Adalto Speroto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2021
Supervisor
Committee
Vargas Junior, Valdivino (President)
Correa, Alejandro Roldan
Grejo, Carolina Bueno
Lebensztayn, Élcio
Mora, Erika Alejandra Rada
Title in Portuguese
Resultados para o modelo de rumor de Maki-Thompson em árvores
Keywords in Portuguese
Árvores aleatórias
Árvores homogêneas
Modelo de Maki-Thompson
Transição de fase
Abstract in Portuguese
Nesta tese, estudamos o modelo de rumor de Maki-Thompson em árvores homogêneas infinitas que é formulado como um processo de Markov a tempo contínuo. Este modelo pode ser definido como um sistema de partículas interagentes representando a disseminação de um boato por indivíduos em uma árvore homogênea. Assumimos que cada indivíduo possa pertencer a uma das três classes em uma população representada por: ignorantes, propagadores e contidos. Um propagador conta o boato a qualquer um de seus vizinhos ignorantes a uma taxa constante. Por outro lado, com a mesma taxa, um propagador torna-se um contido depois de interagir com outro propagador ou um contido. Ainda neste trabalho, estendemos nossa análise a duas generalizações, na primeira supomos que cada propagador deixa de propagar o boato logo após estar envolvido em um determinado número de tentativas frustradas e na segunda estendemos o modelo de Maki-Thompson às árvores aleatórias independentes e identicamente distribuídas. Estudamos condições suficientes sob as quais o boato se extingue ou sobrevive com probabilidade positiva.
Title in English
Results for the model of the Maki-Thompson rumor model in trees
Keywords in English
Homogeous tree
Maki-Thompson model
Phase transition
Randon trees
Abstract in English
In this work, we study the Maki-Thompson rumor model on infinite homogeneous trees which is formulated as a continuous-times Markov chain. This model can be defined as a system of interacting particles representing the spread of a rumor by individuals in a homogeneous tree. We assume that each individual can belong to one of three classes in a population represented by: ignorants, spreaders and stifles. A spreader tells the rumor to any of its ignorant (nearest) neighbors at a constant rate. On the other hand, also at the same rate, a spreader becomes a stifler after interact with other spreader (nearest neighbors) or a stifler. Still in this work, we extend our analysis to two generalizations, in the first one we assume that each propagator stops spreading the rumor right after being involved in a certain number of failed attempts and in the second we extend the Maki-Thompson model to Independent and identically distributed random trees. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.
 
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Publishing Date
2021-06-23
 
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