# Author Archives: James

# Homework #3

The third and final homework, due June 6th.

# Lectures 15-16: Gaussian processes and the Gaussian free field

Everything we covered on Gaussian processes can be found here.

# Lecture 14: Cover times

In this lecture, we studied hitting times, commute times, the effective resistance metric, and cover times of graphs. The book of Aldous and Fill has rather detailed discussions of all these notions. In particular, see Chapter 2, Section 6 for Matthews’ upper and lower bounds on cover times.

# Lectures 9-13

These lectures covered primarily the following four papers:

- Multi-way spectral partitioning and higher-order Cheeger inequalities
- Subexponential Algorithms for Unique Games and Related Problems
- Approximating the Expansion Profile and Almost Optimal Local Graph Clustering
- Finding Small Sparse Cuts Locally by Random Walk

I will post comprehensive lecture notes soon. We only used the subspace enumeration algorithm from (2) and the bulk of our analysis used the Lovasz-Siminovits-style arguments of (3) (see also (4)).

# Homework #2

This homework is due on Monday, May 14th.

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