# Difference between revisions of "Graduate student reading seminar"

Time and place: Friday 2:30PM-4PM, B211

## Electrical networks

February 3: Review 2.1 and 2.2 from the Lyons-Peres book and read 2.3

February 10: Read 2.4 and start reading 2.5

February 17: Read 2.5

February 24: Read 2.6

HW problem: Let $B_N=[-N,N]^2$ and let $E_N=\{(x,y): x=N, |y|\le N\}$ the east side of this box. Consider a simple RW started at (0,0) on the lattice where the jump probabilities are $1/4-\epsilon, 1/4, 1/4+\epsilon, 1/4$ for the W, N, E and S directions ($\epsilon \gt 0$ is fixed). Let $\tau_N$ be the hitting time of the boundary of $B_N$. Show using the machinery of electrical networks that $P(X_{\tau_N}\in E_N)\to 1$. How can you change the aspect ratio of the box so the result stays true?

## Stochastic Calculus

March 2: Read the first section of the lecture notes.

## Determinantal point processes

Determinantal point processes: Chapters 4 and 6

September 13: start reading the HKPV book (Chapter 4). You can also have a look at the other survey articles listed above.

September 20: finish Section 4.2 and go through the first example in 4.3 (non-intersecting random walks)

September 27: Corollary 4.3.3, the rest of the examples in 4.3 and 4.4 (how to generate determinantal processes)

October 4: there is no reading seminar (you should go to the Probability Seminar instead)

October 11: start reading Section 4.5

October 18: existence and the necessary and sufficient condition (4.5)

October 25: there is no reading seminar this week

November 1: simultaneously observable subsets (end of 4.5), 4.6-4.8

November 8: High powers of complex polynomial processes (4.8), uniform spanning trees (6.1)

November 15: Uniform spanning trees cont. (6.1)

November 22: Ginibre ensemble, circular ensemble (.2, 6.4)

## Electrical networks

December 6: Electrical networks. Start reading Chapter 2 of the Lyons-Peres book.

December 13: Continue reading Chapter 2