Mixing times of Markov chain and shuffling

• Grant number: 20/01492-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2020
• End date: March 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Alexsandro Giacomo Grimbert Gallo
• Grantee: Ricardo Teixeira Romanelli
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project, the student will study all the necessary concepts to establish the cutoff phenomenon for Markov chains with finite state space. He will focus on some cards shuffling, like top-to-random shuffle, riffle shuffle, among others. This will be the opportunity to make a bridge between classical topics seen during the undergraduate course, and some more refined concepts which are nowadays widely used in researches concerning stochastic processes. (AU)