Tempos estacionários fortes, acoplamentos, análise de Fourier e propriedades de mistura de cadeias de Markov

• Ano de defesa: 2022
• Autor(a) principal: Gabriela Araujo Ramalho
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Cadeias de Markov; Tempo estacionário forte; acoplamento; análise de Fourier; passeio aleatório; Matemática – Teses; Markov, Processos de – Teses; Passeio aleatório (Matemática) – Teses; Fourier, Análise de – Teses
• Link de acesso: http://hdl.handle.net/1843/44158

The central object of study in this dissertation are the Markov chains in finite state spaces. The objective is present techniques and tools that allow the obtention of upper bounds for the convergence rate of such a chain for its stationary distribution (or equilibrium distribution). We will discuss three here: strong stationary times, couplings and Fourier analysis. During the course, we will keep in mind the example of the random walk on the hypercube to illustrate how the techniques work. In some points we will present details for this example. The techniques, however, are implemented in a context of converging chains with symmetry properties, such as random walks in groups. In addition to the random walk in the hypercube, other examples of Markov modeling chains appear, for example, on the shuffling of cards which can be seen as a random walk in symmetric group.