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 −...
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| 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 |
| 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. |
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