3.1 Introduction
نویسندگان
چکیده
Consider an undirected graph G. A random walk of length l starting at the vertex u is a sequence of vertices u = v0, v1, v2, · · · , vl, where each vi is chosen to be a random neighbor of vi−1 for all i > 0. One considers the distribution of vi for i ≤ l. Intuitively, a random walk can be thought of as choosing a globally random vertex on a graph using only local choices. This is something that people actually do in practice. For example, one might shuffle a deck of cards by repeatedly moving the top card to a random position in the deck. We can model all orderings of the deck as the vertices of a graph with edges corresponding to the operation described above. This process of repeatedly moving the top card can then be thought of as a random walk that provides a more convenient way of shuffling a deck than explicitly choosing 1 of 52! possible orderings. Traditionally, random walks were considered on infinite graphs, and the following result is typical of what was studied.
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تاریخ انتشار 2005