Occasional master courses
On this page you can find information on interesting master courses in stochastics that are offered
outside the regular national programs listed on the Education page. Follow the links for more information.
In this course, we will start the basics of random graphs, starting with the classical random graphs first studied by Erdös and Renyi. In these random graphs, we start with the complete graph on n vertices, and erase edges independently with probability 1-p, where p is the parameter of the model. We will study the phase transition for the largest connected component, which takes place at p=1/n, where the largest connected component jumps from a logarithmic size to a size proportional to the volume of the graph.
After the discussion of the classical random graph, we will discuss extensions and modifications, which have been invented to model so-called complex networks. Complex networks are large networks, such as the networks describing the relations in a large population. In experiments, it has been discovered that such complex networks behave rather differently from the classical random graph.
The main focus of the course is in:
Working with graphs,
Applications of graphs in networks,
Working with random graphs,
Using Coupling and stochastic ordering,
Working with Branching Processes,
Applying Large Deviations and other probability estimates to Random Graphs,
Understanding the notion of a phase transition in the Classical Random Graph,
Networks in applications and working with more realistic models.