Title: Markov chains

Description: In this class, we will go through the classical theory of Markov chains, using mainly the book of Norris. Among other things, we will prove that while performing simple random walk on $\mathbb{Z}$ or $\mathbb{Z}^2$ , the walker returns to the starting point infinitely many times almost surely, while on $\mathbb{Z}^3$, the walker will pay a finite number of visits to the statring point. We will explore many famous examples, some from card shuffling and some from statistical mechanics. We will also follow the book of Levin, Peres and Wilmer to answer questions of the form "how long does it take to shuffle a deck of cards via riffle shuffles".

Prerequisite: Prerequisites: AMS 310 or AMS 311, followed by Real Analysis or Linear Algebra

Credits: 3, S/U grading

Undergraduate Bulletin Course Information

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