Spatial Stochastics
Members of the research group
• Prof. Dr. Dominic Schuhmacher  (publications)  
• Henning Höllwarth, Dipl.Math.  (publications)  
• Fabian Kück, M.Sc.  
• Jörn Schrieber, M.Sc. 
PhD Students
• Henning Höllwarth, Dipl.Math., topic: Statistical inference in point process models  
• Jörn Schrieber, M.Sc., topic: Optimal transport in probability and statistics, joint supervision with Prof. Dr. Anita Schöbel 
Former PhD Students
• Dr. Fabian Kück, Convergence Rates in Dynamic Network Models (2017)  
• Dr. Kaspar Stucki, Invariance properties and approximation results for point processes (2013), joint supervision with Prof. Ilya Molchanov 
Former M.Sc. and B.Sc. Students
• Yi Zhao, M.Sc., A probabilistic look at mutual information with application to point process (2017)  
• Xueqiu Feng, M.Sc., Selective Importance Sampling for Computing the Maximum Likelihood Estimator in Point Process Models (2017)  
• Janne Breiding, B.Sc., Comparison of logistic regression and maximum pseudolikelihood for spatial point processes (2017)  
• Oskar Hallmann, M.Sc., Convergence Rates for Point Processes Thinned by LogitGaussian Random Fields (2016)  
• Florian Heinemann, B.Sc., MetropolisHastings algorithms for spatial point processes (2016)  
• Valentin Hartmann, B.Sc., A GeometryBased Approach for Solving the Transportation Problem with Euclidean Cost (2016)  
• Stephan Meyer, M.Sc., Maximum likelihood estimation of exponential families of stochastic processes (2016)  
• Philipp Möller, M.Sc., Maximum Likelihood Estimation for Spatial Point Processes using Monte Carlo Methods (2016)  
• Burcu Coskun, M.Sc., Statistical Inference of Linear BirthAndDeath Processes (2015)  
• Saskia Schwedes, M.Sc., Konvergenzgeschwindigkeit für MarkovChain Monte Carlo (2015)  
• Xueqiu Feng, B.Sc., A comprehensive overview of linear birthanddeath processes with an outlook to the nonlinear case (2015)  


• Anna Klünker, M.Sc., Tests auf Unabhängigkeit zwischen Punkten und Marken (2015)  
• Alexander Moehrs, B.Sc., Gaußsche Zufallsfelder: Differenzierbarkeit von Pfaden (2015)  
• Philipp Möller, B.Sc., Shuffling measures and the total variation distance to a perfectly randomized deck of cards (2014)  


• Björn Bähre, B.Sc., Numerical computation of L^{2}Wasserstein distance between images (2014)  
• Nicolas Lenz, B.Sc., Universität Bern, Additivity and OrthoAdditivity in Gaussian Random Fields (2013), joint supervision with Dr. David Ginsbourger  
• Jan Schwiderowski, B.Sc., Erwartete Treffzeiten in Markovketten und deren Anwendung auf Glücksspiele mit Sicherungsoption (2013) 
Research topics
Optimal transport in probability and statistics
How different are two spatial structures? This may be answered very generally in terms of the minimum "cost" incurred when transforming one of the objects into the other one. Structures can be anything from images, over point patterns, to geometric bodies. Cost is often specified in terms of (powers of) distances by which (infinitesimal) units of the structure are transported. The picture gives an example of the optimal transportation plan for transforming the underlying grey scale image to a uniform images when using the squared Euclidean distance.
Dynamic random graphs
Dynamic random graphs are a usefull tool to describe complex systems with an underlying network structure which evolves in time. Of particular interest in this area are the asymptotic properties of the dynamic graphs. The spatial structure can be considered to obtain more realistic models for complex systems.
The following images visualize realizations of random graphs in the model by Britton and Lindholm at a fixed time with different distributions for the social indices. Such indices describe the popularity of the nodes (individuals) and are represented by the node sizes.
Continuum percolation for Gibbs point processes
The Boolean model is defined as the union of balls with a fixed radius and
center points that form a homogenous Poisson process in R^d (see the picture below). Each connected
component is called a cluster. One says that the Boolean model percolates if it contains
a cluster with infinite volume (area). It is well known that in dimension larger than or equal to two
there exists a critical intensity for the underlying Poisson process below which the Boolean model almost surely does not percolate
and above which it almost surely does percolate.
What happens if one replaces the Poisson process with a Gibbs point process? For
which models does there exist a similar percolation phase transition, i.e. a critical
parameter such that the percolation probability jumps from zero to one?