Matemática e Embaralhamentos de Cartas: de Mágicas a Cadeias de Markov

• Ano de defesa: 2016
• Autor(a) principal: Paula Mendes Soares Fialho
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Riffle Shuffle; Modelo GSR; Mágica; Cadeias de Markov; Matemática; Markov, Processos de
• Link de acesso: http://hdl.handle.net/1843/EABA-A9FKNW

This work aims to study the mathematical model of Riffle Shuffle, that we will denote by canonical shuffl. The mathematical model for the canonical shuffle is called Gilbert-Shannon-Reeds (GSR) model, in honor of the mathematicians who developed it. Based on an analysis of a magic, we will introduce the concept of rising sequence, which is closely linked to the GSR model. With this concept we will be able to calculatethe probability of getting a specific permutation of cards, after performing several canonical shuffles. The remaining of this work will be dedicated to find the number of consecutive canonical shuffls that approaches the GSR distribution from the uniform distribution. We will develop a study of Markov Chains, relating them with the canonical shuffle.