Stephan Wagner: From hitting times to the Wiener index of trees

Povzetek. We consider the simple random walk on a graph, which at each step moves to one of the neighbours chosen uniformly at random. The hitting time H_{xy} from a vertex x to a vertex y is the average time it takes a simple random walk starting at x to reach y. We present a surprising connection between the hitting time and the Wiener index (sum of all distances between pairs of vertices) of a tree, its ramifications and generalisations.