In this course we will study general point processes and their basic properties. A point process is a stochastic object, which is formally defined as a random counting measure, but in applications point processes are often identified with their support and viewed as a random set of points. In a Poisson point process the points are independent and we will study this fundamental example in great detail. We shall also discuss some examples with interesting dependent, repulsive particles such as determinantal point processes.
Point processes play an important role in many modern areas of probability theory, e.g. as the object of study in random matrix theory (the eigenvalue distribution) and as the generating object for models in stochastic geometry and random graphs. At the end of the course we will get to kno some geometrical models based on the Poisson point process, like random tessellations and the Boolean model.
|
eG