Contents

IAS/Park City Mathematics Institute vii

Preface ix

Lecture 1. Simple Random Walk and Stirling's Formula 1

Lecture 2. Simple Random Walk in Many Dimensions 9

Lecture 3. Self-Avoiding Walk 15

Lecture 4. Brownian Motion 21

Lecture 5. Shuffling and Random Permutations 27

Lecture 6. Seven Shuffles are Enough (Sort of) 33

Lecture 7. Markov Chains on Finite Sets 39

Lecture 8. Markov Chain Monte Carlo 47

Lecture 9. Random Walks and Electrical Networks 53

Lecture 10. Uniform Spanning Trees 63