Brownian Motion and Markov Chains

• Grant number: 23/06150-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2023
• End date: July 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Guilherme Lima Ferreira da Silva
• Grantee: Oseias da Silva Olegario
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/16062-1 - Asymptotic analysis of interacting particle systems and random matrix theory, AP.JP

Abstract

Many phenomena observed in real life science can be seen as performing random movement. Diffusion of pollutants in the air, diffusion of calcium through bones, movement of dust particles, stock prices on the stock exchange are examples of systems that can be modeled by particles that move randomly over time. In this undergraduate research project, we propose the mathematical study and application of Markov chains and Brownian motion as modeling tools for physical phenomena such as those mentioned.