Models and simulation techniques from stochastic geometry

Stochastic geometry is the study of random patterns, whether of points, line segments, or objects. This course will introduce some key concepts and simulation techniques, and illustrate their use in applications. What follows is a brief overview of the course, which it is hoped will be useful orientation. We will focus on probabilistic aspects; this course is planned to be complementary to that of Prof. Møller next week, which will emphasize the statistical side of the story. The lectures will begin at a somewhat basic level, discussing fundamental concepts and ideas. As the lectures progress, this earlier material will be used to expound more recent research. However even the first lecture will refer to recent results. Here is some related general reading (other useful references are mentioned throughout the text):1 Stoyan et al. (1995) is a general reference to stochastic geometry. Barndorff-Nielsen et al. (1999) is a volume of expository essays treating more recent developments. See also the forthcoming monograph of Møller and Waagepetersen (2003) and the recent expository essays edited by Møller (2003).