# Random d-Processes

*by Dr Sanming Zhou*

*Institution:*Department of Mathematics and Statistics, University of Melbourne

*Date: Fri 2nd September 2005*

*Time: 1:05 PM*

*Location: Room 213, Richard Berry Building, The University of Melbourne*

*Abstract*: A random graph process is a process which begins with some starting

graph and repeatedly adds edges randomly according to some stochastic rule. In this talk I will focus on the random graph processes with vertex-degree bounded by a given integer d. Such a process starts from the empty graph; each time a pair of non-adjacent vertices of degree strictly less than d is chosen uniformly at random, and the edge joining such a pair is added to the current graph. In recent years some very impressive results have been obtained by approximating the dynamics of such a process by the solution of an associated system of differential equations. I will try to explain the basic idea of such methods and present answers to a few open problems relating to random 2-processes.

*For More Information:* Mark Fackrell tel. 8344 8053 email: m.fackrell@ms.unimelb.edu.au