Department of

Mathematics


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

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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."