Analytic and numeric essays on one-dimensional stochastic processes

Author(s)

Anderson Augusto Ferreira

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2009-03-31

Examining board members

Jose Fernando Fontanari; Americo Tristao Bernardes; Salomon Sylvain Mizrahi; Miled Hassan Youssef Moussa; Mario Jose de Oliveira

• Advisor: Jose Fernando Fontanari

Abstract

In this thesis, we discuss three problems on dimensional stochastic processes governed by master equation. By Product Matrix Ansatz (MPA) we determine the conditions sufficient to ensure integrability of a new process of diffusion in a medium with impurities. Investigating the spectrum of this model, we compute the critical exponent z that determines how the observable flow to stationary state. In the folowing, we study the classical 6-vertex model defined in two-dimensional diagonal-diagonal matrix transfer as a unidimensional model of traffic with synchronous and asynchronous dinamics. And to finish our work, we study models of diffusion processes of contact, using the theory of Cluster Mean-Field (AU)