Part II: Random Walks in Random Environment

Contents.

• 1 Introduction

  • 1.1 Model

  • 1.2 Examples

• 2 RWRE - d = 1

  • 2.1 Ergodic theorems

  • 2.2 CLT for ergodic environments

  • 2.3 Large deviations

  • 2.4 The subexponential regime

  • 2.5 Sinai’s model: non standard limit laws and aging properties

• 3 RWRE - d > 1

  • 3.1 Ergodic Theorems

  • 3.2 A Law of Large Numbers in $\mathbb{Z}^d$

  • 3.3 CLT for walks in balanced environments

  • 3.4 Large deviations for nestling walks

  • 3.5 Kalikow’s condition

• References

Ofer Zeitouni: zeitouni@math.umn.edu