abstract:
The mathematical analysis of models of particles moving randomly in disordered environments has been very active over the last thirty years. It has uncovered a number of surprising effects and mathematical challenges. We will discuss some of these effects and challenges in this lecture, which intends to provide an overview of the subject.
additional material:
slides of this lecture
abstract:
One way to describe the spread of an infection on networks is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks).
In this talk, random graphs with a given degree distribution and a given expected number of triangles are constructed.
By using these random graphs we
analyze the spread of two types of infection on a network: Infections with a
fixed infectious period and infections for which an infective individual
will infect all or none of its susceptible neighbors. I will explain that
these two types
of infection can be used to give upper and lower bounds for basic properties
(e.g. the probability of extinction) of infections with more general
infectious periods.