Schedule of Lectures
 8/25:

Lecture: Recurrence vs. transience of random walks.
“Bruteforce” proof of recurrence for random walks in
the 1D and 2D grid.

Reading: None.

Scribe notes by Brad Gulko, in preparation.
 8/30 and 9/1: Class canceled.
 9/6:

Lecture: “Bruteforce” proof of transience for random walk in the 3D grid. Proofs of recurrence vs. transience for grids via spectral analysis of torus graphs.

Reading: None.

Scribe notes by Bruno Abrahao.
 9/8: Class canceled due to flooding.
 9/13:
 9/15:

Lecture: Rayleigh monotonicity. Electrical flows in infinite graphs and their relation to recurrence vs. transience. Proof of recurrence for 2D grid using electrical networks.

Reading: Doyle and Snell, Chapter 2.

Scribe notes by Anna Blasiak, in preparation.
 9/20:

Lecture: Proof of transience for 3D grid using electrical networks. Effective resistance, commute time, and cover time. Kirchhoff's matrixtree theorem.

Reading: Doyle and Snell, Chapter 2.

Scribe notes by Pramook Khungurn, in preparation.
 9/22:

Lecture: The matrixtree theorem and effective resistances. Wilson's algorithm for sampling spanning trees.

Reading: Lyons and Peres, Chapter 4.1.
 9/27:
 9/29:
 10/4: