Exercises and Assignments

Pen and Paper: Walk It By Hand Before the Lecture

You work this in class, before any of it is named. It is designed so that you discover the stationary distribution yourself, with nothing but a pencil: you fill in a transition matrix by hand, push a distribution forward step by step, and notice what the numbers settle on before anybody tells you the formula.

• Where Does the Drunkard Sleep? (handed out in class; the PDF is being rewritten): transition probabilities, one- and two-step distributions, and the long-run visit frequencies of a four-node network.

Interactive Demos

• Ladder Lottery: a fixed board, an unpredictable outcome. One knob sets the rungs; the histogram is where two thousand fresh boards put you, and Gap from even measures it. Drag from four rungs to sixty and watch the gap fall from about 0.6 to 0.08 — that is a random walk mixing, seen from the inside.
• Random walk simulator: the karate club by default. Run five thousand steps and watch every bar settle onto its k/2m mark. Then run it on a network with two obvious communities and count how long the walker stays on one side. Then turn the teleport knob up and find where the distance stops falling.

Assignments

Neither graded assignment runs in this module. The Pair Notebook and the Group Mini-Project both cover Modules 2 through 6. The worksheet and the notebook above are practice, not submissions.