Concepts in Stochastic Models and Processes

In September 2023, I gave an introductory talk at K-Garage G++ Math Seminar, a peer seminar on diverse topics in mathematics. I introduced important concepts that appear in probability theory: phase transition, mixing time, cutoff, and metastability.

Abstract

Stochastic models and processes are commonly used to study the behavior of various objects in physics, chemistry, biology, economics, combinatorics, and much more. There are notable phenomena that often arise in such models. We will introduce the notions of phase transition, rapid mixing, cutoff, and metastability, along with their appearance in various models and their Monte Carlo Markov Chains.

Lecture Note

These are hand-written notes for my talk.