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Master's Dissertation
DOI
https://doi.org/10.11606/D.104.2020.tde-09062020-161749
Document
Author
Full name
Ricardo de Jesus Caldas Assis
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Rodriguez, Pablo Martin (President)
Coletti, Cristian Favio
Lopez, Mario Andres Estrada
Title in Portuguese
Percolação Acessível
Keywords in Portuguese
Árvore n-ária
Percolação acessível
Transição de fase
Abstract in Portuguese
Consideramos o modelo de percolação acessível ma árvore n-ária finita de altura h. O modelo é definido associando-se uma variável aleatória contínua Xv para cada vértice v da árvore. A principal questão a ser considerada e estudada é a existência ou não de um caminho de vizinhos mais próximos v0, v1, ...vn, conectando a raiz com a fronteira da árvore, de tal modo que Xv0 < Xv1 < ... < Xvn. O evento definido pela existência desse caminho é chamado de percolação acessível. Neste trabalho estudamos a probabilidade do evento de percolação acessível quando o valor n é dado por n(h) = n(h) = α(h)h em que h é a altura da árvore e α(h) é constante. Os resultados são obtidos fazendo h → ∞. Adicionalmente, discutiremos outros resultados recentes na literatura.
Title in English
Accessible Percolation
Keywords in English
Accessible percolation
n-are tree
Phase Transition
Abstract in English
We consider the accessibility percolation model on the n-ary three height the finite h. The model is defined by associating a continuous random variable Xv for each vertex v inbthe tree. The main issue to consider and study is whether or not there is a nearest neighbor path v0, v1, ..., vn, connecting the root to the tree boundary, such that Xv0 < Xv1 < ... < Xvn. The event defined by the existence of this path is called the accessible percolation. In this paper we study the probability of the accessible percolation event, when n is given by n(h) = α(h)h where h is the height of the tree and α(h) is constant. Results are obtained by making h → ∞. Additionally, we will discuss other recent results in the literature.
 
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Publishing Date
2020-06-10
 
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