On the Move
While here, I'd absolutely love to meet, get to know, trade ideas or collaborate with any Boston/Cambridge readers. Drop a line or come by my office, 32-G630. I'd also welcome advice on where to eat, how to furnish an apartment on the cheap, how to stop getting lost constantly around town and campus, and all that good stuff.
Speaking of getting lost, a small PSA: did you know that in a long random walk on a finite undirected graph, you can expect to appear at any given node with frequency proportional to its degree? A node's location and degree of centrality in the graph are ultimately irrelevant. Equivalently, every edge gets traversed with the same limiting frequency, and with equal frequency in either direction.
Despite its simplicity, this was an eye-popper for me as an undergrad, and my favorite result in our probability seminar, along with the theorem that the harmonic series 1 + 1/2 + 1/3 + ... converges with probability 1 when each term is instead given a random sign.