Random cherry graphs

Random graphs

We have so far seen a number of examples of random processes on networks, including the spread of information, competition between opinions, and random walks. In all these cases, we see that the structure of the network plays an important role in determining the long-term behaviour or final outcome, and the speed of convergence to this outcome. For example, the mixing time of a random walk is d...

Random graphs

We have so far seen a number of examples of random processes on networks, including the spread of information, competition between opinions, and random walks. In all these cases, we see that the structure of the network plays an important role in determining the long-term behaviour or final outcome, and the speed of convergence to this outcome. For example, the mixing time of a random walk is d...

Random Graphs

In this note, we will briefly introduce the subject of random graphs, also known as Erdös-Rényi random graphs. Given a positive integer n and a probability value p ∈ [0, 1], the G(n, p) random graph is an undirected graph on n vertices such that each of the ( n 2 ) edges is present in the graph independently with probability p. When p = 0, G(n, 0) is an empty graph on n vertices, and when p = 1...

Random Graphs

Random Graphs

Once upon a time, I began as an analyst. I studied function spaces such as BMO and operators on function spaces, see for example 6,7], but gradually I became more and more interested in probability theory. Some years ago I worked on random coverings and other problems in geometrical probability 8,9], and at present most of my time is devoted to the related eld of combinatorial probability, in p...