Recorrência, transiência e slow down para o passeio aleatório em ambiente aleatório

Let {αz}z∈Z be a sequence of independent, identically distributed random variables with 0 ≤ αz ≤ 1 for all z ∈ Z. The random walk in a random environment on the integers is the sequence {Xn}n∈N, where X0 = 0 and, inductively, Xn+1 = Xn + 1 with probability αXn and Xn+1 = Xn − 1 with probability 1 −...

Descripción completa

Detalles Bibliográficos
Autor: Weberson da Silva Arcanjo
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Federal de Minas Gerais (UFMG)
Repositorio:Repositório Institucional da UFMG
Idioma:portugués
OAI Identifier:oai:repositorio.ufmg.br:1843/51003
Acceso en línea:http://hdl.handle.net/1843/51003
https://orcid.org/0000-0003-4875-3805
Access Level:acceso abierto
Palabra clave:Passeios Aleatórios
Ambientes Aleatórios
Recorrência
Transiência
Slow Down
Matemática – Teses
Passeio aleatório (Matemática) – Teses
Campos aleatórios – Teses
Descripción
Sumario:Let {αz}z∈Z be a sequence of independent, identically distributed random variables with 0 ≤ αz ≤ 1 for all z ∈ Z. The random walk in a random environment on the integers is the sequence {Xn}n∈N, where X0 = 0 and, inductively, Xn+1 = Xn + 1 with probability αXn and Xn+1 = Xn − 1 with probability 1 − αXn . The objective of this work is to establish a criterion of recurrence and transience for a random walk in random environment in one dimension and study a very interesting phenomenon known as slow down which occurs when we choose a specific distribution for the environment. All the work will be based on the paper Random Walks in a Random Environment, by Fred Solomon, 1975.