Will be taking a sabbatical leave from Rutgers for the academic year 2024-2025. As much as I enjoy teaching, it seems opportune to devote my full effort to research, particularly on Markov chain Mixing Time, Markov chain Monte Carlo, and related topics. Thankful to Dean John Griffin, Associate Dean Suneeta Ramaswami, and Math Department Chair Haydee Herrera-Guzman for their support and helping make this come to fruition.