CMPT 881 - Pseudorandomness : Solutions to Problem Set 1

1. Random walks and Electrical networks Let G be a connected, undirected graph on n vertices, and let s and t be any two distinct vertices of G. For any vertex v of G, let pv denote the probability that a random walk on G starting at the vertex v will visit s before visiting t. (Using a more picturesque language, imagine that G represents a map of some city. A drunken tourist is trying to get to his hotel, represented by the vertex s, by performing a random walk in the city. The vertex t represents a bar. For each point in the city, we are interested in the probability that our tourist will get to his hotel before he gets to the bar (where he would stay all night)).