Contact (Karlsruhe)
Prof. Dr. Günter Last
Karlsruhe Institute of Technology
Institut für Stochastik
Kaiserstraße 89
76133 Karlsruhe
Phone: +49-721-608 43265
Fax: +49-721-608 46691
Contact (Erlangen)
Prof. Dr. Klaus Mecke
Universität Erlangen-Nürnberg
Institut für Theoretische Physik
Staudtstraße 7
91058 Erlangen
Phone: +49-9131-85 28442
Fax: +49-9131-85 28444
Contact (Aarhus)
Department of Mathematical Sciences
Ny Munkegade 118
building 1530
8000 Aarhus C


4. Random fields

Random fields are among the most useful mathematical models of random geometric structures, which can be applied to natural phenomena studied in physics. Of particular interest in statistical physics is the modeling of fluctuating fluid interfaces and noisy patterns, which occur, for instance, in chemical reaction diffusion systems or as intensity maps in gamma-ray astronomy. This project deals with the analysis of level and excursion sets of random fields. A special focus is on the Minkowski functionals of these random sets to gain a better understanding of their geometry. Such an approach can be used to detect high-energy sources in H.E.S.S. sky maps. A further topic of this project are geometric properties of self-similar random processes.

See below for further details on the different subprojects.

Project Members

Cooperating partners



Morphometric analysis in Gamma ray astronomy

H.E.S.S., an array of four imaging atmospheric Cherenkov telescopes for gamma-rays above 100 GeV, observes an increasing number of large extended sources. To account for these additional structures compared to common point source analyses, a new analysis technique based on the morphology of the sky map is developed.

The here presented morphometric data analysis is a new method to detect sources of gamma-ray emission, which is especially designed for the detection of faint structured sources. Minkowski functionals quantify the structure of the count map, which is then compared to the expected structure of a pure Poisson background with gamma-ray sources leading to significant deviations from background structure.

The standard likelihood ratio method of Li and Ma is exclusively based on the number of excess counts and discards all further structure information of large extended sources. The morphometric data analysis incorporates this additional geometric information in an unbiased analysis, i.e. without the need of any prior knowledge about the source.

Pasta matter


At densities below the normal nuclear density, the nearly spherical nuclei lower their total surface area by forming exotic nuclear configurations called pasta shapes. Minkowski functionals identify and characterize the pasta shapes and provide a robust and comprehensive morphological analysis.



  • Klatt, Michael A.
  • Morphometry of random spatial structures in physics
  • FAU University Press, Erlangen 2016
    note: PhD thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg
  • Dennis Müller
  • A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian Excursions
  • Preprint (2016)


  • Bastian Schuetrumpf, Michael A. Klatt, Kei Iida, Gerd E. Schröder-Turk, Joachim A. Maruhn, KLaus Mecke, and Paul-Gerhard Reinhard
  • Appearance of the single gyroid network phase in «nuclear pasta» matter
  • Phys. Rev. C 91, 025801 (2015)


  • Günter Last, Peter Mörters, and Hermann Thorrison
  • Unbiased shifts of Brownian Motion
  • Ann. Probab. 42, 431–463 (2014)
  • Bastian Schuetrumpf, Michael A. Klatt, Kei Iida, Gerd E. Schröder-Turk, Joachim A. Maruhn, Klaus Mecke, and Paul-Gerhard Reinhard
  • Minimal surfaces in nuclear pasta with the time-dependent Hartree-Fock approach
  • PoS Bormio 2014, 032 (2014)


  • Daniel Göring, Michael A. Klatt, Christian Stegmann, and Klaus Mecke
  • Morphometric analysis in gamma-ray astronomy using Minkowski functionals
  • A&A 555, A38 (2013)
  • Michael A. Klatt and Takatoshi Ichikawa and Kei Iida and Naoyuki Itagaki and Joachim A. Maruhn and Kenichi Matsuyanagi and Klaus Mecke and Shigeo Ohkubo and Paul-Gerhard Reinhard and Bastian Schütrumpf
  • Exotic cluster structures in the mean-field theory
  • Journal of Physics: Conference Series 445(1), 012036 (2013)
  • Bastian Schütrumpf, Michael A. Klatt, Kei Iida, Joachim Maruhn, Klaus Mecke, and Paul-Gerhard Reinhard
  • Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature
  • pages 012009 in: Journal of Physics: Conference Series, 2013
    note: for FAIRNESS 2012
  • Bastian Schütrumpf, Michael A. Klatt, Kei Iida, Joachim Maruhn, Klaus Mecke, and Paul-Gerhard Reinhard
  • Time Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature
  • Physical Review C 87, 055805 (2013)


  • Kostya Borovkov and Günter Last
  • On Rice's formula for stationary multivariate piecewise smooth processes
  • J. Appl. Probab. 49, 351–363 (2012)
  • Jürgen Kampf, Günter Last, and Ilya Molchanov
  • On the convex hull of symmetric stable processes
  • Proc. Amer. Math. Soc. 140, 2527–2535 (2012)
  • Michael A. Klatt, Daniel Göring, Christian Stegmann, and Klaus Mecke
  • Shape analysis of counts maps
  • pages 737–740 in: AIP Conference Proceedings, 2012
    note: for 5th Int. Meeting on High Energy Gamma-Ray Astr.