Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, April 8, 2020.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2020             April 2020              May 2020
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7             1  2  3  4                   1  2
8  9 10 11 12 13 14    5  6  7  8  9 10 11    3  4  5  6  7  8  9
15 16 17 18 19 20 21   12 13 14 15 16 17 18   10 11 12 13 14 15 16
22 23 24 25 26 27 28   19 20 21 22 23 24 25   17 18 19 20 21 22 23
29 30 31               26 27 28 29 30         24 25 26 27 28 29 30
31


Wednesday, April 8, 2020

3:30 pm in https://illinois.zoom.us/j/806582029 (email Anush Tserunyan for the password),Wednesday, April 8, 2020

#### Random walks on graphs and spectral radius: part 3

###### Anush Tserunyan (UIUC Math)

Abstract: We will continue discussing random walks on graphs. In this last talk of the series, we will consider recurrence/transience of random walks, proving that this is determined by whether or not the expectation of the number of visits to a fixed vertex is infinite. We will use it to deduce that the simple random walk on nonamenable Cayley graphs is transient. We will also show that the simple random walk on $\mathbb{Z}^d$ is recurrent if and only if $d \le 2$. As Kakutani put it, "A drunk man will find his way home, but a drunk bird may get lost forever."